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

5-136.

Write the equation of the inverse function, f –1(x), for each of the following functions. Homework Help ✎

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

Start by solving for x.
y = log3x
x = 3y
Now 'rename the x and y'.

y = 62x
2x = log6y

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

f −1(x) = ____________

f −1(x) = 3x

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

3. $f(x) = π^2$

Notice that y = π² 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.