find the functions f&g so that fog = H

Question

H(x)=squre root x^2+8

please show work

Answer 1

If you mean H(x) = sqrt(x^2 + 8), the f and g functions could be
g(x) = x^2 +8
and
f(x) = sqrt(x)

But there are other possibilities. For example
g(x) = (x^2 + 8)^2 and
f(x) = x^1/4