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Chapter 7: Problem 37

Evaluate each function at the given value of the variable. \(g(x)=x^{2}+1\) a. \(g(2)\) b. \(g(-2)\)

Short Answer

Expert verified
The values are \( g(2)=5 \) and \( g(-2)=5 \).

Step by step solution

01

Substitute x with 2 in equation

Substitute 2 into the equation \( g(x) \). This gives us the equation \( g(2)=(2)^{2}+1 \). This follows from the function definition \( g(x)=x^{2}+1 \) where \( x=2 \).
02

Solve for \( g(2) \)

Solving for \( g(2) \), we find that \( g(2)=4+1=5 \).
03

Substitute x with -2 in equation

Next, substitute -2 into the equation \( g(-2)=(-2)^{2}+1 \). This also follows from the function definition \( g(x)=x^{2}+1 \) where \( x=-2 \).
04

Solve for \( g(-2) \)

Solving for \( g(-2) \), we find that \( g(-2)=4+1=5 \). Notice that squaring even a negative number will give us a positive result, so both \( g(2) \) and \( g(-2) \) are equal to each other.

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