Question

Hi, I just joined cuz I need help with this problem.... thank you :*

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

-Show your work to prove that the inverse of f(x) is g(x).

- Show your work to evaluate g(f(x)).

- Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

Answer 1

In the 1st equation write
$$
y=\frac{x+a}{b}
$$
Then replace x with y and y with x:
$$
x=\frac{y+a}{b}
$$
Then, solve for y. This is the inverse of \(f(x)\)
You will immediately see what \(c\) and \(d\) should be.

Answer 2

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Answer 3

What numbers should I use?

Answer 4

lol thanks @GretaKnows

Answer 5

I'm using a=5 and b=3.... that's ok right?

Answer 6

Did you check that the function you got was the inverse of the other

Answer 7

This is what i got soo far for part 1 and part 2... I'm not sure if its correct
Part 1:
f(x) = x + 5/3
(g(x) = (x+5)/3

Part 2:
f(x) = 3x -5
Change f(x) for y:
y = 3x -5
Switch the x and y:
x =3y -5
Isolate the y by adding five to both sides:
x + 5 =3y
Divide both sides by 3:
x+5=3y / 3 y=x+5/ 3
That’s how you get:
y = x+5 / 3

Answer 8

When you graph f(x) and g(x) just choose 5 points for each and graph.

Say x=-3, -2, 0, 1, 2

Then graph y=x. You should see that f(x) is a mirror image of g(x) about the line y=x

Answer 9

Wait...... is part 1 and part 2 correct?????

Answer 10

But is it correct or not???

Answer 11

In your Part 1
Given \(a=5\) and \(b=3\)
$$
f(x)=\frac{x+5}{3}
$$
Not
$$
f(x)=x+5/3
$$
Based on your original function.

Be careful when dividing quantities, here we are dividing the entire quantity x+5 b 3, not just dividing 5 by 3.

Make sense?

In Part 2, your process is good, just remember the division issue I just mentioned. Redo it with this in mind.

Answer 12

so i changed it to this..... f(x) = (x+5)/3????

Answer 13

yes and then redo your work using that equation for f(x)