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Evaluating Functions Solutions

• Until now, you have used the substitution property to replace a    variable    in an expression or equation with another    value    (a number, variable, or expression).
• 
Now, you can substitute an entire    function    into another function.

Substitution with Variables	Substitution with Functions
$f\left(x\right)=2x+3$	$f\left(x\right)=2x+3$	$g\left(x\right)=x+4$
$f\left(4\right)=2\left(4\right)+3$	$f\left(g\right(x\left)\right)=2(x+4)+3$
$f\left(x\right)=2x+3$	$f\left(g\right(x\left)\right)=2x+8+3$
	$f\left(g\right(x\left)\right)=2x+11$

Example 1

Given $\mathit{h}\left(\mathit{x}\right)\mathbf{=}\mathbf{–}\mathbf{2}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathit{a}\mathit{x}$ where a is a constant and $\mathit{h}\mathbf{(}\mathbf{–}\mathbf{5}\mathbf{)}\mathbf{=}\mathbf{–}\mathbf{65}\mathbf{,}$ determine h(5).

Example 2

Evaluate the functions f and g with the expression $\mathbf{2}\mathit{n}\mathbf{–}\mathbf{1}\mathbf{.}$

$f\left(x\right)=x^2+4 g\left(x\right)=–x^2+6x$