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Chapter 7: Problem 40

Evaluate each function at the given value of the variable. \(g(x)=-x^{2}+1\) a. \(g(5)\) b. \(g(-4)\)

Short Answer

Expert verified
a. \(g(5) = -24\)\n b. \(g(-4) = -15\)

Step by step solution

01

Substitute \(x=5\) into the function

To find \(g(5)\), replace every occurrence of \(x\) in the function with \(5\). That gives \(g(5) = -(5)^{2} + 1\).
02

Simplify \(g(5)\)

By the order of operations, the exponent must be calculated before the multiplication. Thus, \(g(5) = -25 + 1 = -24\).
03

Substitute \(x=-4\) into the function

To find \(g(-4)\), replace every occurrence of \(x\) in the function with \(-4\). That gives \(g(-4) = -(-4)^{2} + 1\).
04

Simplify \(g(-4)\)

By the order of operations, the exponent must be calculated before the multiplication. Thus, \(g(-4) = -16 + 1 = -15\).

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