Question

f(x)= sqrt(6x-6) and g(x)=6x^2-2

For each function h given below, find a formula for h(x) and the domain of h. Enter the domains using interval notation.

(A) h(x) = (f o g)(x).
h(x) =
Domain =

(B) h(x) = (g o f)(x).
h(x) =
Domain =

(C) h(x) = (f o f)(x).
h(x) =
Domain =

(D) h(x) = (g o g)(x).
h(x) =
Domain =

Answer 1

Do you need help finding the composite function or the domain? To do the first problem you need to find the composite function (f o g)(x). That means find the function f(g(x)). So g(x)=6x^2-2. Substitute that in f(g(x)) and it's f(6x^2-2). Since f(x) = sqrt(6x-2), replace all x with 6x^2-2. You would get f(6x^2-2) = sqrt(6(6x^2-2)-2) Simplify the problem and it's sqrt(36^2-14) So f(6x^2-2)= sqrt(36^2-14). The domain would be all real numbers since parabolas never have a problem. Every x has a y.

Answer 2

Then you just have go through the same process for the rest of the problems