Question

For the given functions f ,g , and h , find fogoh and state the exact domain of fogoh . Please show all of your work.
f(x)=e^x
g(x)=sqrt x
h(x)=2x^2+3x-35

Answer 1

fogoh = fo(goh)

goh = g(h) = sqrt(h) = sqrt(2x^2 + 3x - 35)

fo(goh) = f(goh) = e^sqrt(2x^2 + 3x - 35)

domain of h is all real x

domain of g(x) is x >= 0
so, domain of g(h) = h >= 0 so x <= -5 or x >= 7/2

domain of f is all real x

So, since g is undefined when -5 < x < 7/2, fogoh has the same domain as g