# Chapter 2 - Section 2.1 - Functions - Exercises: 23

Evaluate $f(x) = x^{2}+2x$: $f(0)=0$ $f(3) = 15$ $f(-3) = 3$ $f(a) = a^{2}+2a$ $f(-x) = x^{2}-2x$ $f(\frac{1}{a}) =\frac{1}{a^{2}} +\frac{2}{a}$

#### Work Step by Step

x = 0 $f(0) = 0^{2}+2(0)$ ... square 0 and multiply $2\times0$ $= 0 +0$ ... add $= 0$ ___________________ x = 3 $f(3) = 3^{2}+2(3)$ ... square 3 and multiply $2\times3$ $= 9 +6$ ... add $= 15$ ___________________ x = -3 $f(-3) = (-3)^{2}+2(-3)$ ... square -3 and multiply $2\times(-3)$ $= 9 + (-6)$ ... add $= 3$ ___________________ x = a $f(a) = a^{2}+2(a)$ ___________________ x = -x $f(-x) = (-x)^{2}+2(-x)$ ... square (-x) and multiply $2\times(-x)$ $= x^{2} + (-2x)$ ... simplify $= x^{2} - 2x$ ___________________ x = $\frac{1}{a}$ $f(\frac{1}{a}) = (\frac{1}{a})^{2}+2(\frac{1}{a})$ ... square $\frac{1}{a}$ and multiply $2\times\frac{1}{a}$ $= \frac{1}{a^{2}} +\frac{2}{a}$ ___________________

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