QuestionEvaluate the function $q(x)=\frac{1}{x^{2}-9}$ for (a) $q(0)$ , (b) $q(3)$ , (c) $9(y+3)$ . If undefined, write UNDEFINED.

Studdy Solution

STEP 1

Assumptions1. The function is defined as $q(x)=\frac{1}{x^{}-9}$

STEP 2

To find the function value, we need to substitute the given x value into the function.
(a) For $q(0)$ , we substitute $x=0$ into the function.
$q(0)=\frac{1}{0^{2}-9}$

STEP 3

Calculate the value of the function for $x=0$ .
$q(0)=\frac{1}{0-9}$

STEP 4

implify the expression.
$q(0)=\frac{1}{-9}$

STEP 5

Calculate the value.
$q(0)=\frac{1}{-9} = -\frac{1}{9}$

STEP 6

For $q(3)$ , we substitute $x=3$ into the function.
$q(3)=\frac{1}{3^{2}-9}$

STEP 7

Calculate the value of the function for $x=3$ .
$q(3)=\frac{1}{9-9}$

STEP 8

implify the expression.
$q(3)=\frac{1}{0}$

STEP 9

The value of the function for $x=3$ is undefined because division by zero is undefined in mathematics. So, $q(3)$ is UNDEFINED.

STEP 10

For $q(9(y+3))$ , we substitute $x=9(y+3)$ into the function.
$q(9(y+3))=\frac{}{(9(y+3))^{2}-9}$

STEP 11

implify the expression.
$q(9(y+3))=\frac{}{81(y+3)^{}-9}$ The function value for $q(9(y+3))$ is $\frac{}{81(y+3)^{}-9}$ .

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QuestionEvaluate the function $q(x)=\frac{1}{x^{2}-9}$ for (a) $q(0)$ , (b) $q(3)$ , (c) $9(y+3)$ . If undefined, write UNDEFINED.

Studdy Solution

STEP 1

Assumptions1. The function is defined as $q(x)=\frac{1}{x^{}-9}$

STEP 2

To find the function value, we need to substitute the given x value into the function.
(a) For $q(0)$ , we substitute $x=0$ into the function.
$q(0)=\frac{1}{0^{2}-9}$

STEP 3

Calculate the value of the function for $x=0$ .
$q(0)=\frac{1}{0-9}$

STEP 4

implify the expression.
$q(0)=\frac{1}{-9}$

STEP 5

Calculate the value.
$q(0)=\frac{1}{-9} = -\frac{1}{9}$

STEP 6

For $q(3)$ , we substitute $x=3$ into the function.
$q(3)=\frac{1}{3^{2}-9}$

STEP 7

Calculate the value of the function for $x=3$ .
$q(3)=\frac{1}{9-9}$

STEP 8

implify the expression.
$q(3)=\frac{1}{0}$

STEP 9

The value of the function for $x=3$ is undefined because division by zero is undefined in mathematics. So, $q(3)$ is UNDEFINED.

STEP 10

For $q(9(y+3))$ , we substitute $x=9(y+3)$ into the function.
$q(9(y+3))=\frac{}{(9(y+3))^{2}-9}$

STEP 11

implify the expression.
$q(9(y+3))=\frac{}{81(y+3)^{}-9}$ The function value for $q(9(y+3))$ is $\frac{}{81(y+3)^{}-9}$ .

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QuestionEvaluate the function q(x)=1x2−9q(x)=\frac{1}{x^{2}-9}q(x)=x2−91​ for (a) q(0)q(0)q(0), (b) q(3)q(3)q(3), (c) 9(y+3)9(y+3)9(y+3). If undefined, write UNDEFINED.

Studdy Solution

STEP 1

Assumptions1. The function is defined as q(x)=1x−9q(x)=\frac{1}{x^{}-9}q(x)=x−91​

STEP 2

To find the function value, we need to substitute the given x value into the function.(a) For q(0)q(0)q(0), we substitute x=0x=0x=0 into the function.q(0)=102−9q(0)=\frac{1}{0^{2}-9}q(0)=02−91​

STEP 3

Calculate the value of the function for x=0x=0x=0.q(0)=10−9q(0)=\frac{1}{0-9}q(0)=0−91​

STEP 4

implify the expression.q(0)=1−9q(0)=\frac{1}{-9}q(0)=−91​

STEP 5

Calculate the value.q(0)=1−9=−19q(0)=\frac{1}{-9} = -\frac{1}{9}q(0)=−91​=−91​

STEP 6

For q(3)q(3)q(3), we substitute x=3x=3x=3 into the function.q(3)=132−9q(3)=\frac{1}{3^{2}-9}q(3)=32−91​

STEP 7

Calculate the value of the function for x=3x=3x=3.q(3)=19−9q(3)=\frac{1}{9-9}q(3)=9−91​

STEP 8

implify the expression.q(3)=10q(3)=\frac{1}{0}q(3)=01​

STEP 9

The value of the function for x=3x=3x=3 is undefined because division by zero is undefined in mathematics. So, q(3)q(3)q(3) is UNDEFINED.

STEP 10

For q(9(y+3))q(9(y+3))q(9(y+3)), we substitute x=9(y+3)x=9(y+3)x=9(y+3) into the function.q(9(y+3))=(9(y+3))2−9q(9(y+3))=\frac{}{(9(y+3))^{2}-9}q(9(y+3))=(9(y+3))2−9​

STEP 11

implify the expression.q(9(y+3))=81(y+3)−9q(9(y+3))=\frac{}{81(y+3)^{}-9}q(9(y+3))=81(y+3)−9​The function value for q(9(y+3))q(9(y+3))q(9(y+3)) is 81(y+3)−9\frac{}{81(y+3)^{}-9}81(y+3)−9​.

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QuestionEvaluate the function $q(x)=\frac{1}{x^{2}-9}$ for (a) $q(0)$ , (b) $q(3)$ , (c) $9(y+3)$ . If undefined, write UNDEFINED.

Assumptions1. The function is defined as $q(x)=\frac{1}{x^{}-9}$

To find the function value, we need to substitute the given x value into the function.
(a) For $q(0)$ , we substitute $x=0$ into the function.
$q(0)=\frac{1}{0^{2}-9}$

Calculate the value of the function for $x=0$ .
$q(0)=\frac{1}{0-9}$

implify the expression.
$q(0)=\frac{1}{-9}$

Calculate the value.
$q(0)=\frac{1}{-9} = -\frac{1}{9}$

For $q(3)$ , we substitute $x=3$ into the function.
$q(3)=\frac{1}{3^{2}-9}$

Calculate the value of the function for $x=3$ .
$q(3)=\frac{1}{9-9}$

implify the expression.
$q(3)=\frac{1}{0}$

The value of the function for $x=3$ is undefined because division by zero is undefined in mathematics. So, $q(3)$ is UNDEFINED.

For $q(9(y+3))$ , we substitute $x=9(y+3)$ into the function.
$q(9(y+3))=\frac{}{(9(y+3))^{2}-9}$

implify the expression.
$q(9(y+3))=\frac{}{81(y+3)^{}-9}$ The function value for $q(9(y+3))$ is $\frac{}{81(y+3)^{}-9}$ .