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Chapter 1: Problem 29

Evaluate each function at the given values of the independent variable and simplify. \(g(x)=x^{2}+2 x+3\) a. \(g(-1)\) b. \(g(x+5)\) c. \(g(-x)\)

Short Answer

Expert verified
a) \(g(-1) = 2\) \nb) \(g(x + 5) = x^{2} + 12x + 38\) \nc) \(g(-x) = x^{2} - 2x + 3\)

Step by step solution

01

Evaluate \(g(-1)\)

To find the value of \(g(-1)\), substitute \(x = -1\) into the function equation. So, \[g(-1) = (-1)^{2} + 2(-1) + 3 = 1 - 2 + 3 = 2\]. \(\therefore g(-1) = 2\).
02

Evaluate \(g(x + 5)\)

To find the value of \(g(x + 5)\), substitute \(x + 5\) for \(x\) in the function equation. Hence, \[g(x + 5) = (x + 5)^{2} + 2(x + 5) + 3 = x^{2} + 10x + 25 + 2x + 10 + 3 = x^{2} + 12x + 38\]. \(\therefore g(x + 5) = x^{2} + 12x + 38\).
03

Evaluate \(g(-x)\)

To find the value of \(g(-x)\), substitute \(-x\) for \(x\) in the function equation. So, \[g(-x) = (-x)^{2} + 2(-x) + 3 = x^{2} - 2x + 3\]. \(\therefore g(-x) = x^{2} - 2x + 3\)

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