Math  /  Algebra

QuestionFind (qr)(x)(q \circ r)(x) for q(x)=1x10q(x)=\frac{1}{x-10} and r(x)=4x5r(x)=|4x-5|. What is the domain in interval notation?

Studdy Solution
The function (qr)(x)(q \circ r)(x) is undefined at x=154x = \frac{15}{4} and x=54x = -\frac{5}{4}. Therefore, the domain of (qr)(x)(q \circ r)(x) in interval notation is (,54)(54,154)(154,)(-\infty, -\frac{5}{4}) \cup (-\frac{5}{4}, \frac{15}{4}) \cup (\frac{15}{4}, \infty).
So, the composite function (qr)(x)=4x510(q \circ r)(x) = \frac{}{|4x-5|-10} and its domain is (,54)(54,154)(154,)(-\infty, -\frac{5}{4}) \cup (-\frac{5}{4}, \frac{15}{4}) \cup (\frac{15}{4}, \infty).

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