If N(x) = (f ◦ g ◦ h)(x) and N(x)= equation, find f(x), g(x), and (h)(x).

Question

If N(x) = (f ◦ g ◦ h)(x) and  N(x)= equation, find f(x), g(x), and (h)(x).

smileyxl3 · Answer

equation is $$(\sqrt{2x})^5$$

smileyxl3 · Answer

@Becki

anonymous · Answer

Think of those Russian nesting dolls. You're stacking, smaller inside the bigger. What's the innermost function here?

smileyxl3 · Answer

It's 2x

anonymous · Answer

Yes. Now what's being done to the 2x directly?

smileyxl3 · Answer

It's being squared$$\sqrt{x}$$

anonymous · Answer

It's being rooted, but yes. Your symbol is correct. So what's being done to the root (x)?

smileyxl3 · Answer

power to 5? $$(\sqrt{x})^5$$

anonymous · Answer

Close. The root (x) becomes your x for the next function out.

h(x)=2x
g(x)= root (x)
f(x)= x^5

smileyxl3 · Answer

Ohh... yea I understood how to do it after you showed me but this one had 3 so it threw me off. thanks

anonymous · Answer

Yeah, I agree it can get pretty confusing when you have to go in and in and in!