Question

If f(x) = 5x, what is f–1(x)?

Answer 1

$f(x)=5x\to y=5x$

change x to y, and y to x

$x=5y$

solve for y:

$5y=x\ \ \ |:5\\\\y=\dfrac{x}{5}\to y=\dfrac{1}{5}x$

Answer:

$f^{-1}(x)=\dfrac{1}{5}x$

Answer 2

Please, take just a little more time and write the label "inverse function" like this:

-1

f (x). We want the inverse function of f(x) = 5x.

How to obtain it:

1) replace f(x) by y.

2) interchange x and y: x = 5y

3) solve this result for y: y = x/5

4) replace y with the correct symbol for "inverse function of f:"

-1

f (x) = x/5 (answer)