65.4k views
3 votes
Write the function , √(x^3+6)/√(x^3-9) as a composition of three or more non-identity functions.

User Hnviet
by
8.1k points

1 Answer

3 votes

Answer:


h \circ m \circ n \text{ where } h(x)=√(x) \text{ and } m(x)=1+(15)/(n) \text{ and } n(x)=x^3-9

Explanation:

Ok so I see a square root is on the whole thing.

I'm going to let the very outside function by
h(x)=sqrt(x).

Now I'm can't just let the inside function by one function
g(x)=(x^3+6)/(x^3-9) because we need three functions.

So I'm going to play with
g(x)=(x^3+6)/(x^3-9) a little to simplify it.

You could do long division. I'm just going to rewrite the top as


x^3+6=x^3-9+15.


g(x)=(x^3-9+15)/(x^3-9)=1+(15)/(x^3-9).

So I'm going to let the next inside function after h be
m(x)=1 + (15)/(x).

Now my last function will be
n(x)=x^3-9.

So my order is h(m(n(x))).

Let's check it:


h(m(x^3-9))


h(1+(15)/(x^3-9))


h((x^3-9+15)/(x^3-9))


h((x^3+6)/(x^3-9))


\sqrt{ (x^3+6)/(x^3-9)}

User Jimbeeer
by
8.3k points

No related questions found