Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

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

Answer

$f(x)$ and $g(x)$ are inverse functions.

Work Step by Step

Let us find the inverse of $f(x)$ by solving for $x$. \[ y = \sqrt{x-4} \\ \\ y^2 = x-4 \\ \\ y^2 + 4 = x \] However, notice that the domain of $f(x)$ is from $[4, \infty)$. Therefore, looking at the solution graphically, there cannot be any point on $g(x)$ with a $y$ coordinate of less than 4. Graphically, we see that every point on $f(x)$, when reflected over the line $g(x)$ lies on one point on $g(x)$. Specifically, if a point $(a,b)$ is on $f(x)$, then there is a point $(b, a)$ on $g(x)$.
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