Let f(x)= x^3, g(x) = sqrt x, h(x) = x-4, and j(x)= 2x. Express the following function k as a composite of three of these four functions.

Question

k(x)= sqrt (x^3 - 4)

Do I need to factor anything out of the parentheses or something? If you can, please explain this problem to me :) any help is GREATLY appreciated!!

Answer 1

The composition of functions can be expressed as the function of a function.

Let f(x)=x² and g(x) = x+1,
fog(x) = f(g(x)) = f(x+1)=(x+1)²
gof(x) = g(f(x)) = g(x²) = x²+1

So it is clear that in general fog(x) ≠ gof(x).

You can read more about it in this article:
http://en.wikipedia.org/wiki/Function_composition

Given f(x)= x^3, g(x) = sqrt x, h(x) = x-4, and j(x)= 2x.
You can "compose" the function
m(x) = x³-4 from
m(x)
= hof(x)
= h(f(x))
= h(x³)
= x³-4

Can you take it from here?

Answer 2

Ohhh that makes perfect sense! I don't see how I couldn't see that before. Soooo the answer would be g(h(f(x))), right?

Thanks for your help!! :D :D

Answer 3

Glad to be of help!

Answer 4

this didn’t help me at all. y’all suck .

Answer 5

It’s 2 square 2