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Chapter 1: Problem 27

Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(q(x)=1 /\left(x^{2}-9\right)\) (a) \(q(0)\) (b) \(q(3)\) (c) \(q(y+3)\)

Short Answer

Expert verified
(a) When \(x = 0\), \(q(0) = -1/9\). (b) When \(x = 3\), the function is undefined. (c) When \(x = y+3\), \(q(y+3) = \frac{1}{{y^{2} + 6y}}.

Step by step solution

01

(a) Substituting x = 0

Substitute \(x = 0\) into the function \(q(x) =\frac{1}{{x^{2} - 9}}\): \[q(0) = \frac{1}{{0^{2} - 9}} = -\frac{1}{9}\]
02

(b) Substituting x = 3

Substitute \(x = 3\) into the function \(q(x) = \frac{1}{{x^{2} - 9}}\): \[q(3) = \frac{1}{{3^{2} - 9}}\] Given that \(3^{2}-9 = 0\), this will make the function undefined, so \(q(3)\) is not defined.
03

(c) Substituting x = y + 3

Substitute \(x = y + 3\) into the function \(q(x) =\frac{1}{{x^{2} - 9}}\): \[q(y+3) = \frac{1}{{(y+3)^{2} - 9}} = \frac{1}{{y^{2} + 6y + 9 - 9}} = \frac{1}{{y^{2} + 6y}}\]

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