find possible fuctions

Question

If h(x) = 4+1/(sq root of x-5), find possible functions f and g so that h(x)= (fog)(x). Do not use f(x)=x or g(x)=x. Check solution

Answer 1

Let g(x) = √(x-5), f(x) = 4 + 1/x

 

then, h(x) = (f ο g)(x) = f(g(x)) = f(√(x-5)) = 4 + 1/√(x-5)