How Do You Find (fog)(x) Given F(x)=2x^3-5x^2 And G(x)=2x-1?

How do you find #(fog)(x)# given #f(x)=2x^3-5x^2# and #g(x)=2x-1#? Precalculus Functions Defined and Notation Function Composition

1 Answer

Jim G. Apr 22, 2017

#(2x-1)^2(4x-7)#

Explanation:

#"to evaluate" (f@g)(x)" substitute g(x) into f(x)"#

#f(color(red)(2x-1))#

#=2(color(red)(2x-1))^3-5(color(red)(2x-1))^2#

#"factor out " (2x-1)^2#

#rArr(2x-1)^2[2(2x-1)-5]#

#=(2x-1)^2(4x-7)#

#"which may be further expanded if you wish"#

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