Question

Given that f(x)= -3x^2+x+4 and g(x)=2x-7, determine each of the following. Make sure to fully simplify your answer.A) (f o g)(x)=B) (g o f)(x)=

Answer 1

A)

$(f\circ g)(x)=f(g(x))=f(2x-7)=-3(2x-7)^2+(2x-7)+4$$=-3(4x^2-28x+49)+(2x-7)+4$$=-12x^2+84x-147+2x-7+4$$(f\circ g)(x)=-12x^2+86x-150$

B)

$(g\circ f)(x)=g(f(x))=g(-3x^2+x+4)=2(-3x^2+x+4)-7$$=-6x^2+2x+8-7$$(g\circ f)(x)=-6x^2+2x+1$