SOLUTION: please explain: Find f(x) and g(x) such that h(x) = (f ∘ g)(x). h(x)=√(12x^2+21) Thank you.

Algebra ->  College  -> Linear Algebra -> SOLUTION: please explain: Find f(x) and g(x) such that h(x) = (f ∘ g)(x). h(x)=√(12x^2+21) Thank you.      Log On


   

Question 1140383: please explain:
Find f(x) and g(x) such that h(x) = (f ∘ g)(x). h(x)=√(12x^2+21)
Thank you.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
h%28x%29=sqrt%2812x%5E2%2B21%29

Choose g%28x%29=12x%5E2%2B21, and then f%28x%29=sqrt%28x%29.

h(x) may have other composed possibilities.

Another way:
g(x)=x^2 and then f(x)=sqrt(12x+21) so composing f of g would be replace x with g=x^2, sqrt%2812%28x%5E2%29%2B21%29 and small simplification step.