MATH SOLVE

3 months ago

Q:
# For which pairs of functions is (f•g)(x)=12x? f(x)=3-4x and g(x)=16x-3 F(x)=6x2 and g(x)= 2/xF(x)= and g(x) = 144xF(x)=4x and g(x) =3x

Accepted Solution

A:

Answer:F(x)=4x and g(x) =3xStep-by-step explanation:We will have to check each pair of functions one by oneSo,For f(x)=3-4x and g(x)=16x-3For composition we have to put g(x) in place of x in f(x)(fog)(x)=3-4(g(x))= 3-4(16x-3)=3-64x+12=-64x+15So first pair doesn't give 12x. Now for,F(x)=6x2 and g(x)= 2/x(fog)(x)= 6(g(x))^2=6(2/x)^2=6*(4/x^2)=24/x^2For the last pair:F(x)=4x and g(x) =3x(fog)(x)=4(g(x))=4(3x)=12xSo for the last pair of functions (fog)(x) is 12x ..