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Flashcards: Evaluate functions for inputs in their domains

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

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

The expression is undefined.

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$-\frac{1}{4}$ $\displaystyle -\frac{1}{4}$

$\displaystyle -1$

$- \frac{1}{5}$ $\displaystyle - \frac{1}{5}$

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Flashcards: Evaluate functions for inputs in their domains

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

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

The expression is undefined.

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$-\frac{1}{4}$ $\displaystyle -\frac{1}{4}$

$\displaystyle -1$

$- \frac{1}{5}$ $\displaystyle - \frac{1}{5}$

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Flashcards: Evaluate functions for inputs in their domains

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

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

Your answer:

The expression is undefined.

Your answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Your answer:

$-\frac{1}{4}$ $\displaystyle -\frac{1}{4}$

Your answer:

$\displaystyle -1$

Correct answer:

$- \frac{1}{5}$ $\displaystyle - \frac{1}{5}$

Explanation:

By definition,

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

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

$\displaystyle g(x) = |x+2|$

$\displaystyle g(2) = |2+2| = |4| =4$

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

so evaluate f(4) $\displaystyle f(4)$ through a similar substitution:

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

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

the correct response.

Flashcards: Evaluate functions for inputs in their domains

Define functions $\displaystyle f$ and $\displaystyle g$ as follows:

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

$\displaystyle g(x)= x+ 4$

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

Undefined

$\displaystyle 14$

$\displaystyle 7$

$\displaystyle 0$

$\displaystyle 2$

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Flashcards: Evaluate functions for inputs in their domains

Define functions $\displaystyle f$ and $\displaystyle g$ as follows:

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

$\displaystyle g(x)= x+ 4$

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

Your answer:

Undefined

Your answer:

$\displaystyle 14$

Your answer:

$\displaystyle 0$

Your answer:

$\displaystyle 2$

Correct answer:

$\displaystyle 7$

Explanation:

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

$\displaystyle g(x)= x+ 4$

$\displaystyle g(0)= 0+ 4= 4$

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

$\displaystyle f(x)= x+ 3$

$\displaystyle f(4)= 4+ 3 = 7$ ,

the correct value.

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