Evaluate functions for inputs in their domains - HiSet: High School Equivalency Test: Math

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Question

Define $f(x)= -\frac{1}{x+1}$ and .

Evaluate $(f\circ g )(2)$ .

Answer

By definition,

$(f\circ g )(2) = f(g(2))$ ,

so first, evaluate by substituting 2 for in :

$(f\circ g )(2) = f(4)$ ,

so evaluate through a similar substitution:

$f(x)= -\frac{1}{x+1}$

$f(4)= -\frac{1}{4+1} = - \frac{1}{5}$ ,

the correct response.

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Question

Define functions and as follows:

$f(x)= \left{\begin{matrix} x^{2} -2,&x< 0 \ x+ 3,& x \ge 0\end{matrix}\right.$

Evaluate $(f \circ g)(0)$ .

Answer

By definition, $(f \circ g)(0) = f(g(0))$ . Evaluate by substituting 0 for in the definition of :

$(f \circ g)(0) = f(g(0)) = f(4)$ , so substitute 4 for in the definition of . Since 4 satisfies the condition $x \ge 0$ , use the definition for those values:

,

the correct value.

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