College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.1 - Exponential Functions - 4.1 Exercises: 10

Answer

$g(-\frac{1}{2})\approx 0.650$; $g(\sqrt6) \approx 8.281$; $g(-3)\approx 0.075$; $g(\frac{4}{3}) \approx 3.160$

Work Step by Step

Evaluate the function for the given values of $x$ by substituting each $x$ into $g(x)$ then using a calculator to find the exact value. When x=$-\frac{1}{2}$: $g(x) = \left(\dfrac{4}{3}\right)^{3x} \\g(-\frac{1}{2})=\left(\dfrac{4}{3}\right)^{3(-\frac{1}{2})} \\g(-\frac{1}{2})=\left(\dfrac{4}{3}\right)^{-\frac{3}{2}} \\g(-\frac{1}{2})\approx 0.650$ When $x=\sqrt6$: $g(x) = \left(\dfrac{4}{3}\right)^{3x} \\g(\sqrt6) = \left(\dfrac{4}{3}\right)^{3(\sqrt6)} \\g(\sqrt6) = \left(\dfrac{4}{3}\right)^{3\sqrt6} \\g(\sqrt6) \approx 8.281$ When $x=-3$: $g(x)=\left(\dfrac{4}{3}\right)^{3x} \\g(-3)=\left(\dfrac{4}{3}\right)^{3(-3)} \\g(-3)=\left(\dfrac{4}{3}\right)^{-9} \\g(-3)\approx 0.075$ When $x=\frac{4}{3}$: $g(x)=\left(\dfrac{4}{3}\right)^{3x} \\g(\frac{4}{3}) = \left(\dfrac{4}{3}\right)^{3(\frac{4}{3})} \\g(\frac{4}{3}) = \left(\dfrac{4}{3}\right)^{4} \\g(\frac{4}{3}) \approx 3.160$
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