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3.4 Exercise 46

Avg difficulty 2.5

Use each set of functions to find f( g( h(x) ) ). f \left(g \left(h \left(x\right)\right)\right) . Simplify your answers.

Given functions p(x)= 1 x p \left(x\right) = \frac{1}{\sqrt{x}} and m(x)= x 2 −4, m \left(x\right) = x^{2} - 4 , state the domain of each of the following functions using interval notation:

  1. ⓐ p(x) m(x) \frac{p \left(x\right)}{m \left(x\right)}
  2. ⓑ p(m(x)) p \left(m \left(x\right)\right)
  3. ⓒ m(p(x)) m \left(p \left(x\right)\right)

OpenStax Algebra and Trigonometry 2e, 3.4 Composition of Functions, exercise 46

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Adapted from College Algebra © 2021 Rice University. Licensed under CC BY 4.0. Sources: College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e, College Algebra with Corequisite Support 2e. Imported at revision 4922e46.