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3.4 Exercise 44

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 f(x)= 2−4x f \left(x\right) = \sqrt{2 - 4 x} and g(x)=− 3 x , g \left(x\right) = - \frac{3}{x} , find the following:

  1. ⓐ (g∘f)(x) \left(g \circ f\right) \left(x\right)
  2. ⓑ the domain of (g∘f)(x) \left(g \circ f\right) \left(x\right) in interval notation

OpenStax Algebra and Trigonometry 2e, 3.4 Composition of Functions, exercise 44

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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.