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Chapter 7: Problem 38

Evaluate each function at the given value of the variable. \(g(x)=x^{2}+4\) a. \(g(3)\) b. \(g(-3)\)

Short Answer

Expert verified
The evaluation of the function \(g(x)\) for inputs 3 and -3 both yield the same output, \(g(3)=g(-3)=13\).

Step by step solution

01

Substitution for \(g(3)\)

Replace \(x\) with 3 in the function \(g(x)=x^{2}+4\). So, \(g(3)\) becomes \(g(3)=3^{2}+4\).
02

Evaluation for \(g(3)\)

Evaluate the expression by calculating the square and addition. This results in \(g(3)=9+4=13\).
03

Substitution for \(g(-3)\)

Now, substitute -3 for \(x\) in the original function, which means \(g(-3)\) becomes \(g(-3)=(-3)^{2}+4\).
04

Evaluation for \(g(-3)\)

After substituting the negative value, the notation indicates that the negative sign should be included in the squaring. So, \((-3)^{2}=9\), and then adding 4, we get \(g(-3)=9+4=13\).

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