Find lim_(x rarr-3)g(x) for g(x)=sqrt(7x+22).

Identify function and point: Identify the function and the point at which we need to find the limit. We have the function g(x) = sqrt(7x+22) and we need to find the limit as x approaches -3.Substitute value into function: Substitute the value of x into the function to see if the function is defined at that point. Let's substitute x = -3 into the function: g(-3) = sqrt(7(-3) + 22) = sqrt(-21 + 22) = sqrt(1).Check if result is real number: Check if the result from Step 2 is a real number. Since sqrt(1) is a real number (specifically, 1), the function is defined at x = -3.Conclude the limit: Conclude the limit based on the previous steps. Since the function is defined at x = -3 and we have a real number as a result, the limit of g(x) as x approaches -3 is simply the value of the function at x = -3.

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Find
lim_(x rarr-3)g(x) for

g(x)=sqrt(7x+22).

Find $\lim _{x \rightarrow-3} g(x)$ for $\newline$ $g(x)=\sqrt{7 x+22} \text {. }$

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Algebra 1

Domain and range of square root functions: equations

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Q. Find

\lim _{x \rightarrow-3} g(x)

for

\newline

g(x)=\sqrt{7 x+22} \text {. }

Identify function and point: Identify the function and the point at which we need to find the limit. $\newline$ We have the function $g(x) = \sqrt{7x+22}$ and we need to find the limit as $x$ approaches $-3$ .
Substitute value into function: Substitute the value of $x$ into the function to see if the function is defined at that point. $\newline$ Let's substitute $x = -3$ into the function: $g(-3) = \sqrt{7(-3) + 22} = \sqrt{-21 + 22} = \sqrt{1}$ .
Check if result is real number: Check if the result from Step $2$ is a real number. Since $\sqrt{1}$ is a real number (specifically, $1$ ), the function is defined at $x = -3$ .
Conclude the limit: Conclude the limit based on the previous steps. $\newline$ Since the function is defined at $x = -3$ and we have a real number as a result, the limit of $g(x)$ as $x$ approaches $-3$ is simply the value of the function at $x = -3$ .