Question

Given f(x) = 4x + 1 all over 3, solve for f^-1(4).

a. 2
b. 4
c. 6
d. 8

Answer 1

Okay, firstly. We need to find the inverse of f(x). Do you know how to do this?

Answer 2

No, could you explain?

Answer 3

Okay, what you need to do first is replace the f(x) with a y. You should get an equation that looks kinda like this.

\(y=4x+1\)

Then you need to solve for x.

When you have done this, you swap the places of y and x. Think you could do this for me?

Answer 4

x = y -1 all over 4?

Answer 5

\(y=4x+1\)

\(y-1=4x\)

\(\displaystyle \frac{y-1}{4}=x\)

Then you forgot the last step, you replace the x with the y.

\(\displaystyle \frac{x-1}{4}=y\)

Then we have,

\(\displaystyle f(x)=\frac{x-1}{4}\)

Do you know how to solve from there?

Answer 6

\(\displaystyle f^{-1}(x)=\frac{x-1}{4}\)

My apologies, I used the wrong notation. My bad.

Answer 7

I understand that part but how would I go from there?

Answer 8

\(\bf f^{-1}({\color{red}{ x}})=\cfrac{{\color{red}{ x}}-1}{4}\qquad \qquad f^{-1}({\color{red}{ 4}})=\cfrac{{\color{red}{ 4}}-1}{4}\)

Answer 9

Oh I see, so the solution would be 4?

Answer 10

is it?

Answer 11

No, do like @jdoe0001 said

\(\bf f^{-1}(\color{red}{4})\)

This just means that you plug in 4 for all instances of x in the function.

Answer 12

f^-1(4) = 3/4?

Answer 13

I would agree.

Answer 14

I don't get where I am supposed to go from here.

Answer 15

Um... wait... those are your options above? They make no sense. None of them can be a possible answer.
@jdoe0001 any thoughts?

Answer 16

ohhh shoot.. I see the mistake..

tis was a typo I gather
ok

so \(\bf f(x)={\color{red}{ y}}=\cfrac{4{\color{blue}{ x}}+1}{3}\qquad inverse\implies {\color{blue}{ x}}=\cfrac{4{\color{red}{ y}}+1}{3}\\ \quad \\
\textit{solve for "y"}\)

Answer 17

hmmm it says \(\bf f^{-1}(3)\ not \ f^{-1}(4)\) btw

Answer 18

My sincere apologies!

Answer 19

I just noticed

Answer 20

Son of a....

@FlowerOfLife you need to use proper formatting.

IN THE BEGINNING

\(\displaystyle \bf f(x)=\frac{4x+1}{3}\)

That makes a difference.

Answer 21

I'm so sorry, I'm not quite sure how to use proper formatting.

Answer 22

@FlowerOfLife so solve for "y"

multiply both sides by 3
then subtract 1 from both
then divide by 4 both

Answer 23

If you aren't sure how to use \(\bf \LaTeX\), something as simple as f(x)=(4x+1)/3 is better than saying "all over"

It is super easy to lose that when looking at a problem.

And, not to nit-pick, you solve for x :P

Answer 24

So then the answer still is not 4?

Answer 25

\(\displaystyle \bf f(x)=\frac{4x+1}{3}\)

\(\displaystyle \bf y=\frac{4x+1}{3}\)

\(\displaystyle \bf x=\frac{3y-1}{4}\)

\(\displaystyle \bf f^{-1}(x)=\frac{3x-1}{4}\)

\(\displaystyle \bf f^{-1}(\color{red}{3})=\frac{3(\color{red}{3})-1}{4}=\frac{9-1}{4}=\frac{8}{4}=2\)

Answer 26

Again sorry for all the confusion u_u

Answer 27

No problem, glad we caught it and put you on the right path! Don't want you to learn the wrong stuff :P