Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.1 - Functions - Exercises: 21

Answer

Evaluate $ f (x) = \frac{1-2x}{3} $: $$ f (2) = -1 $$ $$ f (-2) = \frac{5}{3} = 1.6667 $$ $$ f (\frac{1}{2}) = 0$$ $$ f (a) = \frac{1-2(a)}{3}$$ $$ f (-a) = \frac{1+2a}{3} $$ $$ f (a-1) = \frac{-2}{3}a + 1 $$

Work Step by Step

x = 2 $$ f (2) = \frac{1-2(2)}{3} $$ multiply $2\times(2)$ $$ f (2) = \frac{1-4}{3} $$ subtract $1-4$ $$ f (2) =\frac{-3}{3} $$ divide $\frac{-3}{3}$ $$ f (2) = -1 $$ -------------------------- x = -2 $$ f (-2) = \frac{1-2(-2)}{3} $$ multiply $2\times(-2)$ $$ f (-2) = \frac{1-(-4)}{3} $$ subtract $1-(-4)$ $$ f (-2) =\frac{5}{3} $$ divide $\frac{5}{3}$ $$ f (-2) = 1.6667 $$ -------------------------- x = $\frac{1}{2}$ $$ f (\frac{1}{2}) = \frac{1-2(\frac{1}{2})}{3} $$ multiply $2\times(\frac{1}{2})$ $$ f (\frac{1}{2}) = \frac{1-1}{3} $$ subtract $1-(1)$ $$ f (\frac{1}{2}) =\frac{0}{3} $$ divide $\frac{0}{3}$ $$ f (\frac{1}{2}) = 0 $$ -------------------------- x = a $$ f (a) = \frac{1-2(a)}{3} $$ -------------------------- x = -a $$ f (-a) = \frac{1-2(-a)}{3} $$ multiply $2\times(-a)$ $$ f (-a) = \frac{1-(-2a)}{3} $$ $$= \frac{1+2a}{3} $$ -------------------------- x = a - 1 $$ f (a-1) = \frac{1-2(a-1)}{3} $$ multiply $2\times(a-1)$ $$ f (a-1) = \frac{1-(2a-2)}{3} $$ subtract $1-(2a-2)$ or add $1+ (-2a + 2)$ $$ f (a-1) =\frac{-2a+3}{3} $$ divide and simplify $\frac{-2a+3}{3}$ $$ f (a-1) = \frac{-2}{3}a + \frac{3}{3}$$ $$ = \frac{-2}{3}a + 1$$ --------------------------
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