Define g o fx for the folowing two functions fx2x1 gxx2 Mul

Define (g o f)(x) for the folowing two functions: f(x)=2x-1; g(x)=x^2 . Multiple choice a. 4x^2-4x+1 b. 2x^2-2x+1 c. 4x^2-1 d. 4x^2+4x-1 Show work

Solution

Given

f(x)=2x-1; g(x)=x^2

gof(x) = g( f(x) )

= g( 2x-1 )

= ( 2 x - 1 )^2

gof(x) = ( 2x )^2 - 2 ( 2x ) ( 1 ) + 1^2

gof(x)   = 4 x^2 - 4 x + 1