### Home > CALC > Chapter 5 > Lesson 5.3.3 > Problem5-136

5-136.

Find the inverse function, $f^{ −1} (x)$, for each of the following functions.

1. $f(x) =\operatorname{log}_3x$

Start by solving for $x$.
$y =\operatorname{log}_3x$
$x = 3^y$
Now 'rename the $x$ and $y'$.

$f^{ −1}(x) = 3^x$

1. $f(x) = 6^{2x}$

$y = 6^{2x}$
$2x =\operatorname{log}_6y$
$x=\frac{\text{log}_6y}{2}$
$f^{−1}(x) =$ ____________

1. $f(x) = π^2$

Notice that $y = π^²$ is a horizontal line. What is the inverse of a horizontal line?

1. $f(x) = a^x + k$

Refer to hint in part (b).

Before you convert to a logarithm, subtract $k$ from both sides.