Evaluate functions for inputs in their domains - HiSET

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Question

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

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

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

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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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Question

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

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

Tap to reveal answer

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

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

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

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

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

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

Tap to reveal answer

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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