Home > PC3 > Chapter 5 > Lesson 5.2.3 > Problem5-87

5-87.

​Let $f(x)=3^x$. Evaluate each of the following expressions, or state “impossible” and explain why. It may be helpful to first replace $f$ and $f^{−1}$ with their definitions.

1. $f(4)$

$f(4) = 3^4$

1. $f^{-1}(81)$

This means you need to solve $3^x=81$.

1. $f(-2)$

$f(-2)=3^{-2}$

1. $f^{-1}\left(\frac{1}{9}\right)$

$f(?)=\frac{1}{9}$

1. $f\left(\frac{1}{2}\right)$

$f\left(\frac{1}{2}\right)=3^{1/2}$

1. $f^{-1}\left(\sqrt{3}\right)$

$f(?)=\sqrt{3}$