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$g(x)={[2^(x)-1," for "-8 <= x],[sqrtx," for "x >= 1]:} Find lim_(x rarr4)g(x). Choose 1 answer: (A) 1 (B) 2 (C) 15 (D) The limit doesn't exist.$

$g(x)=\left\{\begin{array}{ll} 2^{x}-1 & \text { for }-8 \leq x \\ \sqrt{x} & \text { for } x \geq 1 \end{array}\right.$ $\newline$ Find $\lim _{x \rightarrow 4} g(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $2$ $\newline$ (C) $\mathbf{1 5}$ $\newline$ (D) The limit doesn't exist.

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Domain and range of absolute value functions: equations

Full solution

Q.

g(x)=\left\{\begin{array}{ll} 2^{x}-1 & \text { for }-8 \leq x \\ \sqrt{x} & \text { for } x \geq 1 \end{array}\right.

\newline

Find

\lim _{x \rightarrow 4} g(x)

.

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

2

\newline

(C)

\mathbf{1 5}

\newline

(D) The limit doesn't exist.

Determine piecewise function for $x$ approaching $4$ : We need to determine which piece of the piecewise function $g(x)$ applies when $x$ is approaching $4$ . The function $g(x)$ is defined as $2^{x}-1$ for $x \leq -8$ and as $\sqrt{x}$ for $x \geq 1$ . Since $4$ is greater than $4$ $1$ , we will use the $\sqrt{x}$ part of the function to find the limit as $x$ approaches $4$ .
Calculate limit of $\sqrt{x}$ as $x$ approaches $4$ : Now we calculate the limit of $\sqrt{x}$ as $x$ approaches $4$ . The limit of a square root function is the square root of the limit point, provided the limit point is within the domain of the function. Since $4$ is within the domain of $\sqrt{x}$ , we can directly substitute $x$ with $4$ .
Substitute $x$ with $4$ in $\sqrt{x}$ to find limit: Substituting $x$ with $4$ in $\sqrt{x}$ gives us $\sqrt{4}$ , which equals $2$ . Therefore, the limit of $g(x)$ as $x$ approaches $4$ is $2$ .

More problems from Domain and range of absolute value functions: equations

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\newline

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\newline

\newline

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\newline

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Posted 3 months ago

Question

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\newline

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What is the domain of this function?

\newline

(8,–1)(7,–11)(–4,10)(4,3)

\newline

\newline

(A)\{–4,4,7,8\}\newline

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What is the domain of this function?

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\newline

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Question

What is the domain of this function?

\newline

(1,–4)(9,–12)(–6,11)(7,5)

\newline

\newline\\(A)\{–6,1,7,9\}\newline

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