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.

pay attention in your classes and concentrate the best thing you can do to raise your test scores is to pay attention when you're supposed to be learning the material: in class!

take good notes.

do your homework.

use mnemonics and other tricks.

do practice tests.

note: the best i know.