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: 79


(a) $f(x)=-2x^2-x+3$ (b) $f(3)=-18$

Work Step by Step

(a) function notation. Solve for $y$: \begin{array}{ccc} &y+2x^2&=&3-x \\&y+2x^2-2x^2&= &3-x-2x^2 \\&y&=&-2x^2-x+3 \end{array} Let $y=f(x)$. The equation becomes: $$f(x)=-2x^2-x+3$$ (b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain: $f(x)= -2x^2-x+3 \\f(3) = -2(3^2)-3+3 \\f(3)=-2(9)-3+3 \\f(3)=-18-3+3 \\f(3)=-18$
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