Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.3 Functions - 2.3 Exercises - Page 217: 81


(a) $f(x) = \frac{4}{3}x-\frac{8}{3}$ (b) $f(3) = \frac{4}{3}$

Work Step by Step

(a) function notation. Solve for $y$: \begin{array}{ccc} &4x-3y&=&8 \\&4x-3y-4x&= &8-4x \\&-3y&=&-4x+8 \\&\frac{-3y}{-3}&=&\frac{-4x+8}{-3} \\&y&=&\frac{4}{3}x-\frac{8}{3} \end{array} Let $y=f(x)$. The equation becomes: $$f(x)=\frac{4}{3}x-\frac{8}{3}$$ (b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain: $f(x)= \frac{4}{3}x-\frac{8}{3} \\f(3) = \frac{4}{3}(3)-\frac{8}{3} \\f(3)=4-\frac{8}{3} \\f(3)=\frac{12}{3}-\frac{8}{3} \\f(3)=\frac{4}{3}$
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