### Home > APCALC > Chapter 6 > Lesson 6.2.1 > Problem6-64

6-64.

Let $f(x) = e^x$, so that $f ^{–1}(x) = \ln(x)$. Write an expression for each of the composite functions below, then simplify. Homework Help ✎

1. $f( f^{ –1}(x))$

Do you remember the definition of inverse functions?
$f(x)$ and $g(x)$ are inverses if $f(g(x))=g(f(x)) = x$...
Well, $f(f ^{−1}(x)) = e^{\ln x }$ ______

1. $f ^{–1}( f (x))$

Refer to the hint in part (a).

1. $f( f ^{–1}(3x))$

Refer to the hint in part (a).

1. $f ^{–1}( f(3x)$

Let 3x = U.