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

5-136.

Write the equation of the inverse function, $f ^{–1}\left(x\right)$, for each of the following functions.

1. $f (x) = \log_3(x)$

Start by solving for $x$.
$y=\log_3x$
$x = 3^{y}$
Now 'rename the $x$ and $y'$.

$y = 6^{2x}$
$2x=\log_6y$

$x=\frac{\text{log}_6y}{2}$

$f ^{−1}\left(x\right) = \text{____________}$

$f ^{−1}\left(x\right) = 3^{x}$

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

3. $f(x) = π^2$

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

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

Refer to hint in part (b).

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