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Chapter 1: Problem 30

Evaluate each function at the given values of the independent variable and simplify. \(g(x)=x^{2}-10 x-3\) a. \(g(-1)\) b. \(g(x+2)\) c. \(g(-x)\)

Short Answer

Expert verified
\[ \begin{align*} g(-1) &= 8, \ g(x+2) &= x^{2} - 6x - 19, \ g(-x) &= x^{2} + 10x - 3 \end{align*}\]

Step by step solution

01

Evaluate \(g(-1)\)

To evaluate \(g(-1)\), substitute \(-1\) into the function \(g(x) = x^{2}-10x-3\). This gives: \(g(-1) = (-1)^{2}-10(-1)-3 = 1 + 10 - 3 = 8\)
02

Evaluate \(g(x+2)\)

To evaluate \(g(x+2)\), substitute \((x+2)\) into the function \(g(x) = x^{2}-10x-3\). This gives: \(g(x+2) = (x+2)^{2}-10(x+2)-3 = x^{2} + 4x + 4 -10x - 20 - 3 = x^{2} - 6x - 19\)
03

Evaluate \(g(-x)\)

To evaluate \(g(-x)\), substitute \(-x\) into the function \(g(x) = x^{2}-10x-3\). This gives: \(g(-x) = (-x)^{2}-10(-x)-3 = x^{2} + 10x - 3\)

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