Question

If f(x) = 5x, what is f–1(x)?

Answer 1

${f}^{ - 1} (x) = switching \: the \: x \: for \\ the \: y \\ f(x) = 5x - - > x = 5y \\ solve \: for \: y. \: {f}^{ - 1} (x) = \frac{x}{5}$

Answer 2

Answer:

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

Step-by-step explanation:

$f^{-1}(x)$ is the inverse function of $f(x)$, that is, if $f(x)$ transform "a" to "b", then $f^{-1}(x)$ transform "b" to "a".

thus:

$f(x)= 5x\\\\y = 5x \ \ \ \ \ \ \ \ \ \ \ Making \ f(x)=y \\\\\frac{y}{5}= x \ \ \ \ \ \ \ \ \ \ \ divide \ both \ sides \ by \ 5\\\\x=\frac{y}{5} \\\\so \ f^{-1}(y) =\frac{y}{5}$

due to the choice of variable is arbitrary, we can write this like:

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