For the given functions f and g , find the indicated composition.

Question

f(x) =-2x+7, g(x) = 6x+7

(g.f)(x)

Answer 1

g composed with f, you need to plug f into g.

g(f(x) = 6(-2x+7)+7 Now simplify by distributing

g(f(x) = -12x+42+7 combine like terms

g(f(x) = -12x+49

Answer 2

f=f(x)= -2x+7

g=g(x) = 6x+7

f(g)=(fog)(x) = f(g(x))

replace g(x) with 6x+7

=f(6x+7)

replace x with 6+7 in f(x)=-2x+7

= -2(6x+7)+7

= -12x-7

f(g(x)) =(fog)(x) = -12x+7

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

replace f(x) with -2x+7

=g(-2x+7)

=6(-2x+7)+7

=-12x+42+7

g(f(x))=-12x+49