Thread: Forming the Compositions f(g(h(x)))

Hello MHF

So I have been working with functions. They have been pretty simple so far.

Like...
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

Therefore domain is (-inf,+inf).

Can someone confirm that I did the triple composition correctly?

Originally Posted by UC151CPR

Hello MHF

So I have been working with functions. They have been pretty simple so far.

Like...
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?

...

Oh yah, my mistake. I accidently wasn't thinking and multiplied x by 4x^2 instead of just substituting it, so I should have gotton

4x^2 - 1 as the composition

thanks