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: 78


(a) $f(x)=\frac{x}{4}-2$ (b) $f(3)=-\frac{5}{4}$

Work Step by Step

(a) function notation. Solve for $y$: \begin{array}{ccc} &x-4y&=&8 \\&x-4y-x &= &8-x \\&-4y&=&-x+8 \\&\frac{-4y}{-4} &= &\frac{-x+8}{-4} \\&y&=&\frac{-x}{-4} + \frac{8}{-4} \\&y&=&\frac{x}{4} -2 \end{array} Let $y=f(x)$. The equation becomes: $$f(x)=\frac{x}{4} -2$$ (b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain: $f(x)= \frac{x}{4}-2 \\f(3) = \frac{3}{4}-2 \\f(3)=\frac{3}{4}-\frac{8}{4} \\f(3)=-\frac{5}{4}$
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