Determine whether the statements are True or False. Justify your answer with an explanation.
If f(x) = x + 1 and g(x) = 6x, then (f ○ g)(x) = (g ○ f)(x).
If you are given two functions f(x) and g(x), you can calculate (f ○ g)(x) if and only if the range of g is a subset of the domain of f.
Problem 1
Answer: False---------------------------------
Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
===============================================
Problem 2
Answer: True---------------------------------
Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
The given statement is false.
What is composite function ?Composite function is a combination of two or more than two functions combined by mathematical operation of addition,subtraction,multiplication and division.Where output of one function is input to the other function.
According to the given question two functions are given f(x) and g(x) and and we have to compose in different order and see if they are same or not.
Given, f(x) = x + 1 and g(x) = 6x
So, (fog)(x) is, output of g(x) is the input of f(x) which is
f(6x) = (6x) + 1
f(6x) = 6x + 1.
Now, (gof)(x) is, output of f(x) is now input of g(x) which is
g(x+1) = 6(x+1)
g(x+1) = 6x + 6.
Thus we can see fog(x) ≠ gof(x).
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Ben made some apple pies. For every 4 cups of butter, he added 3 cups of water. The ratio of butter to water in Ben’s apple pies is ____.
3 over 4
4 over 3
3
4
Answer:
i think 3:4 dont take my word for it thoughn
Step-by-step explanation:
Wha is the property fr each one pls aswer Asap
9514 1404 393
Answer:
A. Given; B. multiplication; C. distributive; D. collect terms; E. addition; F. division
Step-by-step explanation:
You are expected to compare each line to the previous line and identify the changes. Apart from combining like terms (collecting terms), there are generally only three properties of interest: distributive property, addition property, multiplication property. Of course, subtraction and division are just addition and multiplication using the appropriate (additive, multiplicative) inverse.
The distributive property involves adding or deleting parentheses, so it is easy to identify.
If terms disappear, it can be due to terms being combined, or due to addition/subtraction. If coefficients disappear, it will generally be due to multiplication/division.
__
-2.5(-2-3x)+2.5(-4x-1) = -2x -4x . . . . Given
-5(-2 -3x) +5(-4x -1) = -4x -8x . . . . multiplication by 2 (fractions eliminated)
10 +15x -20x -5 = -4x -8x . . . . distributive property (eliminate parentheses)
-5x +5 = -12x . . . . collect terms
5 = -7x . . . . addition of 5x (-5x term disappeared)
-5/7 = x . . . . division by -7 (x coefficient of -7 disappeared)
find the root of the equation:5-6 of=-1
Answer: The answer is 5 1/2
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST!
11/12 times 7 equals what in a fraction
Answer: 77/12
Step-by-step explanation:
1) 11/12 * 7 = (11*7)/12 = 77/12
There are 2 squares and 4 triangles. What is the simplest ratio of squares to total shapes?
Answer:
2:6
Simplest= 1:3
On a coordinate plane, a triangle has points D (negative 2.5, 5), E (0, negative 1), and F (negative 5, negative 1).
What is the y-coordinate of point D after a translation of (x, y) → (x + 6, y – 4)?
D′(3.5,___ )
Answer:
D = (3.5,1)
Step-by-step explanation:
(-2.5,5) is given
you must do (x+6,y-4)
x y
(-2.5,5)
-2.5+6=3.5
x=3.5
5-4=1
y=1
(3.5,1)
Answer:
(3.5, 1)
Step-by-step explanation:
edg 2021
Which of the following is the graph of y=sqrt x+1?
Answer:
B
Step-by-step explanation:
The graph for y= √x+1 is shown below.
What is the square root function?The square root function f(x)=√x has domain [0,∞) with range [0,∞).
Similarly the given function is y=f(x)= √x+1
From the graph, it is clear that the function is valid for x≥0 because x<0 √x will be imaginary.
So the domain of the function f(x)= √x+1 will be [0,∞).
As we know,
√x ≥0
⇒ √x+1≥0+1
⇒√x+1 ≥ 1
⇒f(x) ≥ 1
the function f(x) has range [1,∞).
f(x)=√x+1 ha y intercept at x=0
f(0)= √0+1=1
f(x) has y intercept at (0,1).
Function F(x) will increase from point (0,1).
Therefore The graph for y= √x+1 is shown below.
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A gym's membership in 2012 was 9,300. The current membership is 2,800. Which expression can be used to find the
percent of change?
Answer:
Find the difference between the two, divide by the years, and should get the percent of change
Step-by-step explanation:
The change in percentage is 69.89%.
Given that, a gym's membership in 2012 was $9,300.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
The current membership is $2,800.
We know that, the percentage change = (New value - Original value)/Original value × 100
Now, the percentage change = (9300-2800)/9300 × 100
= 6500/9300 × 100
= 0.6989 × 100
= 69.89%
Therefore, the change in percentage is 69.89%.
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which programming language was used in the first generation conputer
I:machine language
2:assembly language
3:high level language
3:natural language
Answer:
machine language
Step-by-step explanation:
The computers in this generation used machine code as the programming language.
The machine language also referred to as the native language of the computer system is the first generation programming language. In the machine language, a programmer only deals with a binary number. They are translation free and can be directly executed by the computers.
Miles records the time it takes to download a variety of file types. How is the download time related to that file size? How can you show that two quantities have a proportional relationship?
Answer:
answer is 5 minutes
Step-by-step explanation:
Solve the equation.
m2 = 43
Is that 2m=43 or m^2=43??
If 2m=43 then...
m=43/2
m=21.5
If m^2=43 then...
m=√43
Answer:m=21.5
Step-by-step explanation:
5 × -92 =
Just a quick response on how to solve this, thanks a ton!
5 × -92 =
Just a quick response on how to solve this, thanks a ton!
Answer:
-460
Answer: -460
Step-by-step explanation:
Log2 x + log2 (6-x)=3 solve for x algebraically
Answer:
The solution is x = 2 and x = 4
Step-by-step explanation:
Let us revise some rules in logarithmic function:
[tex]log_{a}(x)+log_{a}(y)=log_{a}(xy)[/tex]The logarithmic function is the inverse of the exponential function [tex]log_{b}(c)=a[/tex] is the inverse of [tex]b^{a}=c[/tex]Let us solve the question
∵ [tex]log_{2}(x)+log_{2}(6-x)=3[/tex]
→ By using the first rule above
∴ [tex]log_{2}(x)(6-x)=3[/tex]
→ Multiply x by (6 - x)
∵ x(6 - x) = x(6) - x(x) = 6x - x²
∴ [tex]log_{2}(6x-x^{2})=3[/tex]
→ Change the logarithmic function to exponential function using
the second rule above
∴ [tex]2^{3}=(6x-x^{2})[/tex]
∵ 2³ = 8
∴ 8 = 6x - x²
→ Add x² to both sides
∴ x² + 8 = 6x
→ Subtract 6x from both sides
∴ x² - 6x + 8 = 0
→ Factorize it into 2 brackets
∴ (x - 2)(x - 4) = 0
→ Equate each factor by 0 to find the values of x
∵ x - 2 = 0
→ Add 2 to both sides
∴ x = 2
∵ x - 4 = 0
→ Add 4 to both sides
∴ x = 4
∴ The values of x are 2 and 4
∴ The solution of the equation is x = 2 and x = 4
BD = 8 and AB = 4 Find AD
Answer:
AD is 12
Step-by-step explanation:
Answer:
AD=12
Step-by-step explanation:
AB=4
BD=8
AD=AB+BD
AD=4+8
AD=12
Hope this helps :)
Find the quotient
6 1/2 divided by 3 2/3
Answer:
Step-by-step explanation:
Free points ig
The solution is : the quotient 6 1/2 divided by 3 2/3 is 1 17/22.
Here, we have,
given that,
6 1/2 divided by 3 2/3
Given the following mathematical expression;
6 1/2 / 3 2/3
We would apply the law of indices for fractions.
6 1/2 / 3 2/3
= 13/2 / 11/3
=13*3/ 2*11
=39/22
=1 17/22
Hence, The solution is : the quotient 6 1/2 divided by 3 2/3 is 1 17/22.
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is the line liner?
someone help i need this to pass
Answer:
yes
Step-by-step explanation:
Identify the segment bisector of MN. Then find MN.
Answer:
Segment bisector: JK
MN = 52
since the 26 is right on a little line, tick mark or wtv, im no sure if MN= 78 or 52 but i'd just put 52. Sorry if im
wrongStep-by-step explanation:
Segment bisector is the line in half
The segment bisector of MN is JK and the measure of MN is 52.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
The only bisector of MN is JK and it is at the midpoint of the line segment MN so it will be a bisector.
Now,
Since JK is the bisector of MN
M(JK) = (JK)N
26 = (JK)N
So,
MN = 2(26) = 52
Hence "The segment bisector of MN is JK and the measure of MN is 52".
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Which equation is equivalent to 2x + 3y = 12?
plz plz plz plz plz plpz help mee
Answer:
175
Step-by-step explanation:
x / 7
100 (the mean goal)
100 + 65 + 120 + 150 + 90 + 0 + y = 700
100 + 65 + 120 + 150 + 90 + 0 + 175 = 700
700 / 7
100
The area of a rectangle is x^2 - 6x - 7 with a width of x - 7. What is the lenght?
[tex] {x}^{2} - 6x - 7 = (x - 7)(x + 1) \\ [/tex]
[tex]width = (x - 7)[/tex]
So
[tex]length = (x + 1)[/tex]
Just it...
So we're done.
Thanks for watching buddy good luck.
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y=ax2+bx+c standard form
Answer:
y=3x^2+12x+13
a=3
b=12
c=13
Step-by-step explanation:
Bijou Museum sells 75% of its tickets for the regular price of $14. The remaining discount tickets are sold for the price of $10. Variable cost per guest is $2 for both groups, and fixed costs total $66,000 per month. What are the number of regular-price guests and discount guests at the breakeven point?
Answer:
Regular price guests = 3300
Discount price guests = 1100
Step-by-step explanation:
Breakeven point is the point where total revenue and total cost are equal.
Now, we know total cost is $66,000 per month.
Now, we are told that the museum sells 75% of its tickets for the regular price of $14.
If the total number of tickets is x. It means the number of regular tickets guests is 75%x = 0.75x
We are told that variable cost per guest in each group is $2. This means that total revenue from regular tickets guest is;
14(0.75x) + 2(0.75x) = 12x
Now, the remaining tickets are discount tickets sold for $10.
It means number of discount tickets guests = 0.25x
Total revenue from discount tickets =
10(0.25x) + 2(0.25x) = 3x
Thus, at break even point, we have;
12x + 3x = 66000
15x = 66000
x = 66000/15
x = 4400
Thus;
Regular price guests = 0.75 × 4400 = 3300
Discount price guests = 0.25 × 4400 = 1100
What does losing 100 points do to an A-? What will my overall grade be after I lose the points?
I don’t know if this is different for other countries but I’m in America.
Answer:
Well from all the exams and assignments I've had, 100 points is the full grade so losing 100 points would mean you would fail with a 0
can anyone answer this?
Answer:
it is J
Step-by-step explanation:
What is the slope of the linear function y= - 5/3 - x
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 3 .
Step-by-step explanation:
brainliest please
You need two bottles of fertilizer to treat the flower garden shown. How many bottles do you need to treat a similar garden with a perimeter of 105 feet? A flower garden in the form of trapezoid is shown. The length of longer base is labeled 18 feet, shorter base is 15 feet, height is 4 feet, and one leg is 5 feet.
Answer:
26.25 bottles
Step-by-step explanation:
A flower garden in the form of trapezoid is shown. The length of longer base is labeled 18 feet, shorter base is 15 feet, height is 4 feet, and one leg is 5 feet.
Formula for perimeter of a trapezoid = Side a + side b + length a + length b
For the trapezium shown, its perimeter step 1,
we have to find the missing length
Length a
We are given height = 4 feet
Length of the longer base = 18 feet
Length of the shorter base = 15 feet
Different would give us the base of the right angle triangle
= 18 - 15 = 3 feet
Using Pythagoras Theorem we can find the side a = c
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
c = √25
c = 5 feet
Hence side a = 5 feet
Perimeter of the Trapezoid shown =
18 feet + 15 feet + 5 feet + 5 feet
= 38 feet.
From the question,
You need two bottles of fertilizer to treat the flower garden shown. How many bottles do you need to treat a similar garden with a perimeter of 105 feet
Hence:
38 feet = 2 bottles
105 feet = x bottles
Cross y
= 38 × x = 105 × 2
= 38x = 105 × 2
x = 105 × 2/38
x = 26.25 bottles
26.25 bottles of fertilizer is needed to treat the garden with a perimeter of 105
The sun is about 8 light minutes away. What is the distance
in meters?
Given: Distance to sun: 8 light minutes
speed of light: 3x10^8 m/s
(1 minute=60 seconds)
Unknown: Distance to sun in meters (in scientific notation)
If Jeremy is feeding his Chihuahua 1/2 cup of dog food but uses 1/10 of a cup, how many scoops will he need to feed his dog?
Answer: 5
Step-by-step explanation:
The question is asking how many tenths are in one half. You need to divide one half by one tenth. To divide fractions you need to invert and multiply.
1/2 ÷ 1/10
Step 1: Invert and multiply
1/2 × 10/1 = 10/2
Step 2: Simplify
10/2 = 5
5x2 - 50 + x, when x =4
Answer:
44
Step-by-step explanation:
5*2=10-50=40+4=44