If F(x)=2x-5 And G(x)=x^2+1, What Is G(f(x))? | Socratic

If #f(x)=2x-5# and #g(x)=x^2+1#, what is g(f(x))? Precalculus Functions Defined and Notation Function Composition

1 Answer

Narad T. Jan 5, 2017

The answer is #=4x^2-20x+26#

Explanation:

This is a composition of functions

#f(x)=2x-5#

#g(x)=x^2+1#

#g(f(x))=g(2x-5)=(2x-5)^2+1#

#=4x^2-20x+25+1=4x^2-20x+26#

#f(g(x))=f(x^2+1)=2(x^2+1)-5#

#=2x^2+2-5=2x^2-3#

#g(f(x))!=f(g(x))#

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