# Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises: 27

$f(x)$ has an inverse function.

#### Work Step by Step

We find the derivative of $f(x)$: $f'(x) = \frac{1}{x-3} , x \gt; 3$ We see that on the domain of $f(x)$, $(3, \infty)$, $f'(x)$ is always positive so $f(x)$ is strictly monotonic.

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