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Performing Algebraic Operations on Functions

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Find and simplify the functions ( g−f )( x ) \left(g - f\right) \left(x\right) and ( g f )( x ), \left(\frac{g}{f}\right) \left(x\right) , given f( x )=x−1 f \left(x\right) = x - 1 and g( x )= x 2 −1. g \left(x\right) = x^{2} - 1. Are they the same function?

OpenStax Algebra and Trigonometry 2e, 3.4 Composition of Functions, exercise 7

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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.