Question

Find f^-1(x). Given f(x) = x^3 +7

thanksss

Answer 1

oh okay, is that really how easy it is? I get it!

Answer 2

By f^-1 do you mean f(x) to the negative first power? If so the answer above is correct. But this notation is also used for the inverse function which is different.

Answer 3

yes f(x) to the negative power

Answer 4

or wait is says f to the negative one (x)

Answer 5

Yah I think Sid made a boo boo. A -1 within the function notation is NOT an exponent.
It's the notation for the inverse function, as vinn mentioned.

Let's try that again. :3

Answer 6

\[\large f(x)=x^3+7\]Let y=f(x),\[\large y=x^3+7\]To find the inverse, we swap the x's and y's.\[\large x=y^3+7\]And from here we want to solve for y.
Subtract 7 from each side,\[\large y^3=x-7\]Taking the cube root of each side,\[\large y=\sqrt[3]{x-7}\]

\[\large f^{-1}(x)=\sqrt[3]{x-7}\]

Answer 7

i'm thinking this through for a secound

Answer 8

k np ^^

Answer 9

okay. I think I understand, I just watched the Khan academy video

Answer 10

Ah good, those are helpful videos.

Answer 11

Like Zep said. That notation means inverse. The process is:
1) Switch x and y
2) Solve for y

Answer 12

okay, I get it now. I switch x and y and then solve for why and then I solve

Answer 13

how do I find an inverse function though?

Answer 14

step by step answers posted here http://www.mathskey.com/question2answer/4106/find-f-1-x
ask your Algebra1 homework questions at http://www.mathskey.com/question2answer/algebra-1 and get free math help. all the best

Answer 15

And the way you can think about that is this:
A function's inverse is sort of the "opposite." The function takes in inputs and gives out outputs. The inverse goes in the other direction, making the outputs the inputs and vice-versa. Here's an example:
f(x) = y could be a function that takes in the amount of gas you buy and tells you the price you pay.
x, the input, is amount of gas. Y, the output is cost.

The inverse of the function would go in the opposite direction, meaning instead of taking in the amount of gas as the input, it would take in the amount of money you spent. And the output now would be how much gas you bought.

Answer 16

\(\large y\) was the letter we chose to represent our function \(\large f(x)\).
After we swap the letters, this \(\large y\) in the equation now represents \(\large f^{-1}(x)\).

I'm sorry I didn't explain that very well in my last step, I simply rewrote the y as f^-1(x).

Answer 17

okay okay. I understand. So I will always switch x and y when dealing with functions?

Answer 18

Yes =)

Answer 19

okay great. Thank you all so much!