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

5-136.

Find the inverse function,

*f*^{−1}(*x*), for each of the following functions. Homework Help ✎*f*(*x*) = log_{3}*x**f*(*x*) = 6^{2}^{x}*f*(*x*) =*π*^{2}*f*(*x*) =*a*+^{x}*k*

Start by solving for *x*.*y* = log_{3}*x**x* = 3^{y}

Now 'rename the *x* and *y*'.

*f* ^{−1}(*x*) = 3^{x}

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

*y* = 6^{2}^{x}

2*x* = log_{6}*y*

*f* ^{−1}(*x*) = ____________

Refer to hint in part (b).

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