Chapter 1.2, Problem 37E

To determine

To Evaluate: The function at specified value of the independent variable and simplify.

Answer to Problem 37E

  $q(-3)=0$ , $q(2)=-\frac{1}{5}$, $q(y+3)=\frac{1}{y(y+6)}$

Explanation of Solution

Given: $q(x)=\frac{1}{x-9}$

  $(a)q(-3)(b)q(2)(c)q(y+3)$

Given: $q(x)=\frac{1}{x-9}$

Now

  $(a)q(-3)$

Substitute $x=-3$

  $\begin{array}{l}q(x)=\frac{1}{x-9}\\ q(-3)=\frac{1}{(-3)-9}\\ q(-3)=\frac{1}{9-9}\\ q(-3)=0\end{array}$

  $(b)q(2)$

Substitute $x=2$

  $\begin{array}{l}q(x)=\frac{1}{x-9}\\ q(2)=\frac{1}{(2)-9}\\ q(2)=\frac{1}{4-9}\\ q(2)=-\frac{1}{5}\end{array}$

  $(c)q(y+3)$

Substitute $x=y+3$

  $\begin{array}{l}q(x)=\frac{1}{x-9}\\ q(y+3)=\frac{1}{(y+3)-9}\\ q(y+3)=\frac{1}{y^2+9+6y-9}\\ q(y+3)=\frac{1}{y^2+6y}\\ q(y+3)=\frac{1}{y(y+6)}\end{array}$

Hence,

  $q(-3)=0$ , $q(2)=-\frac{1}{5}$, $q(y+3)=\frac{1}{y(y+6)}$