Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.

f(x)=(x + a)/b

g(x) = cx - d

next: show your work to prove that the inverse of f(x) is g(x).

then: show your work to evaluate f(g(

last: graph your two functions on a coordinate plane. include a table of values for each function. graph the line y = x on the same graph.

Answers can vary.

This is a very open question.

The ones I chose was

When I did I got the expression back.

The graphs are in the attachment.

Step-by-step explanation:

To find the inverse we mainly just need to swap and . Afterwards, we will solve for the new .

Let's begin that process.

Multiply both sides by :

Subtract on both sides:

So the inverse of is .

Comparing this to their inverse which is , we see whatever we choose for the value that's what needs to be and whatever we choose for will be the value of .

So that is in general the inverse of is .

We should get and if they are indeed inverses.

Let's verify:

That verifies .

That verifies .

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Part 1:

So let's pick and .

So this means and .

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Part 2:

We are asked to show what simplifies to.

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Part 3:

has slope 4 or 4/1 and -intercept -1.

So I will draw a dot at -1 on the -axis.

From there, I will rise 4 and go right 1 and put another dot.

I also rewrite 4/1 as -4/-1 and so from the -intercept I went down 4 and left 1 also and put a dot.

has been colored purple.

or has slope 1 and -intercept 0.

So I will draw a dot at 0 on the -axis.

I will then plot another point by using the slope for this line. The slope is 1 or 1/1 so from the -intercept I will got up 1 and right 1 and put another dot.

is in red.

or has -intercept is 1/4 and slope is 1/4.

Draw a dot at on the -axis.

I then use the slope 1/4 to graph another point by rising up 1 and going over 4 from the -intercept and putting another dot.

I also wrote 1/4 as -1/-4 and went down 1 and left 4 from the -intercept and put another dot.

is in blue.

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Another way to graph is use a table of points.

x  | y=f(x)                      | (x,y)

---------------------------------------------

-5 |  (-5+1)/4=(-4)/4=-1     | (-5,-1)

0  |  (0+1)/4=1/4             |  (0,1/4)

3  |  (3+1)/4=4/4=1          |  (3,1)

We could graph these points for and then form a straight line with them.

x  | y=g(x)                    | (x,y)

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-1  |  4(-1)-1=-4-1=-5       | (-1,-5)

1/4 | 4(1/4)-1=1-1=0        | (1/4,0)

1    | 4(1)-1=4-1=3          |  (1,3)

We could graph these points for and then form a straight line with them.

I put these dots in pink on my graph.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1