QuestionEvaluate $(q \circ r)(x)$ for $q(x)=\frac{1}{x-10}$ and $r(x)=|4x-5|$ . What is the domain?

Studdy Solution

STEP 1

Assumptions1. The function $q(x)$ is given by $q(x)=\frac{1}{x-10}$ . The function $r(x)$ is given by $r(x)=|4x-5|$
3. We need to find the composite function $(q \circ r)(x)$ , which means we need to substitute $r(x)$ into $q(x)$ .

STEP 2

The composite function $(q \circ r)(x)$ is defined as $q(r(x))$ . So, we need to substitute $r(x)$ into $q(x)$ .
$(q \circ r)(x) = q(r(x))$

STEP 3

Substitute $r(x)$ into $q(x)$ .
$(q \circ r)(x) = q(|x-5|)$

STEP 4

Replace $x$ with $|4x-|$ in the function $q(x)$ .
$(q \circ r)(x) = \frac{1}{|4x-|-10}$ This is the composite function $(q \circ r)(x)$ .

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