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HiSET: Math : Evaluate functions for inputs in their domains

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Example Question #1 : Evaluate Functions For Inputs In Their Domains

Define $f(x)= -\frac{1}{x+1}$ and g(x) = |x+2| .

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

Possible Answers:

The expression is undefined.

$\frac{1}{3}$

$- \frac{1}{5}$

$-\frac{1}{4}$

Correct answer:

$- \frac{1}{5}$

Explanation:

By definition,

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

so first, evaluate g(2) by substituting 2 for in g(x) :

g(x) = |x+2|

g(2) = |2+2| = |4| =4

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

so evaluate f(4) 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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Example Question #1 : Evaluate Functions For Inputs In Their Domains

Define functions and as follows:

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

g(x)= x+ 4

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

Possible Answers:

Undefined

Correct answer:

Explanation:

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

g(x)= x+ 4

g(0)= 0+ 4= 4

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

f(x)= x+ 3

f(4)= 4+ 3 = 7 ,

the correct value.

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HiSET: Math : Evaluate functions for inputs in their domains

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #1 : Evaluate Functions For Inputs In Their Domains

Example Question #1 : Evaluate Functions For Inputs In Their Domains

All HiSET: Math Resources

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