QuestionEvaluate $(q \circ p)(x)$ for $p(x)=x^{2}-9x$ and $q(x)=\frac{1}{x-10}$ . What is the domain?

Studdy Solution

STEP 1

Assumptions1. The function $p(x)$ is defined as $p(x) = x^{}-9x$ . The function $q(x)$ is defined as $q(x) = \frac{1}{x-10}$
3. The composition of functions $(q \circ p)(x)$ is defined as $q(p(x))$

STEP 2

To find the composition of functions $(q \circ p)(x)$ , we need to substitute $p(x)$ into $q(x)$ .
$(q \circ p)(x) = q(p(x))$

STEP 3

Substitute $p(x)$ into $q(x)$ .
$(q \circ p)(x) = q(x^{2}-9x)$

STEP 4

Replace $x$ in $q(x)$ with $p(x)$ .
$(q \circ p)(x) = \frac{1}{(x^{2}-9x)-10}$

STEP 5

implify the expression.
$(q \circ p)(x) = \frac{1}{x^{2}-9x-10}$ This is the composition of functions $(q \circ p)(x)$ .

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QuestionEvaluate $(q \circ p)(x)$ for $p(x)=x^{2}-9x$ and $q(x)=\frac{1}{x-10}$ . What is the domain?

Studdy Solution

STEP 1

Assumptions1. The function $p(x)$ is defined as $p(x) = x^{}-9x$ . The function $q(x)$ is defined as $q(x) = \frac{1}{x-10}$
3. The composition of functions $(q \circ p)(x)$ is defined as $q(p(x))$

STEP 2

To find the composition of functions $(q \circ p)(x)$ , we need to substitute $p(x)$ into $q(x)$ .
$(q \circ p)(x) = q(p(x))$

STEP 3

Substitute $p(x)$ into $q(x)$ .
$(q \circ p)(x) = q(x^{2}-9x)$

STEP 4

Replace $x$ in $q(x)$ with $p(x)$ .
$(q \circ p)(x) = \frac{1}{(x^{2}-9x)-10}$

STEP 5

implify the expression.
$(q \circ p)(x) = \frac{1}{x^{2}-9x-10}$ This is the composition of functions $(q \circ p)(x)$ .

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QuestionEvaluate (q∘p)(x)(q \circ p)(x)(q∘p)(x) for p(x)=x2−9xp(x)=x^{2}-9xp(x)=x2−9x and q(x)=1x−10q(x)=\frac{1}{x-10}q(x)=x−101​. What is the domain?

Studdy Solution

STEP 1

Assumptions1. The function p(x)p(x)p(x) is defined as p(x)=x−9xp(x) = x^{}-9xp(x)=x−9x . The function q(x)q(x)q(x) is defined as q(x)=1x−10q(x) = \frac{1}{x-10}q(x)=x−101​3. The composition of functions (q∘p)(x)(q \circ p)(x)(q∘p)(x) is defined as q(p(x))q(p(x))q(p(x))

STEP 2

To find the composition of functions (q∘p)(x)(q \circ p)(x)(q∘p)(x), we need to substitute p(x)p(x)p(x) into q(x)q(x)q(x).(q∘p)(x)=q(p(x))(q \circ p)(x) = q(p(x))(q∘p)(x)=q(p(x))

STEP 3

Substitute p(x)p(x)p(x) into q(x)q(x)q(x).(q∘p)(x)=q(x2−9x)(q \circ p)(x) = q(x^{2}-9x)(q∘p)(x)=q(x2−9x)

STEP 4

Replace xxx in q(x)q(x)q(x) with p(x)p(x)p(x).(q∘p)(x)=1(x2−9x)−10(q \circ p)(x) = \frac{1}{(x^{2}-9x)-10}(q∘p)(x)=(x2−9x)−101​

STEP 5

implify the expression.(q∘p)(x)=1x2−9x−10(q \circ p)(x) = \frac{1}{x^{2}-9x-10}(q∘p)(x)=x2−9x−101​This is the composition of functions (q∘p)(x)(q \circ p)(x)(q∘p)(x).

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QuestionEvaluate $(q \circ p)(x)$ for $p(x)=x^{2}-9x$ and $q(x)=\frac{1}{x-10}$ . What is the domain?

Assumptions1. The function $p(x)$ is defined as $p(x) = x^{}-9x$ . The function $q(x)$ is defined as $q(x) = \frac{1}{x-10}$
3. The composition of functions $(q \circ p)(x)$ is defined as $q(p(x))$

To find the composition of functions $(q \circ p)(x)$ , we need to substitute $p(x)$ into $q(x)$ .
$(q \circ p)(x) = q(p(x))$

Substitute $p(x)$ into $q(x)$ .
$(q \circ p)(x) = q(x^{2}-9x)$

Replace $x$ in $q(x)$ with $p(x)$ .
$(q \circ p)(x) = \frac{1}{(x^{2}-9x)-10}$

implify the expression.
$(q \circ p)(x) = \frac{1}{x^{2}-9x-10}$ This is the composition of functions $(q \circ p)(x)$ .