So I have been working with functions. They have been pretty simple so far.
EXAMPLE: Form the composition f(g(x)) and give the domain:
f(x) = 2^2 + x
g(x) = sqrt(x)
So f(g(x)) = [sqrt(x)]^2 + sqrt(x) = x + sqrt(x)
Therefore domain is [0,+inf)
BUT what if we have3 functions and we are trying to create a composition? I just want to make sure I am doing this right...
EXAMPLE: Form the composition f(g(h(x))) and give the domain:
f(x) = x -1
g(x) = 4x
h(x) = x^2
So f(g(h(x))) = f(g(x^2)) = f(4x^3) = 4x^3 -1
g(x^2) = 4x^2, not 4x^3
Therefore domain is (-inf,+inf).
Can someone confirm that I did the triple composition correctly?