Let h(x)=x^3 + 1
Determine functions f(x) and g(x) such that h(x)=f(g(x)) [Do not use f(x)=x or g(x)=x]

Question

Let h(x)=x^3 + 1  
Determine functions f(x) and g(x) such that h(x)=f(g(x))    [Do not use f(x)=x  or g(x)=x]

unklerhaukus · Answer

$$g(x)=x^3$$$$f(x)=x+1$$

$$h(x)=f \circ g=f(g(x))=f(x^3)=x^3+1$$

anonymous · Answer

That makes sense, thank you for your help.

unklerhaukus · Answer

i think there could be a few different $f(x)$'s and $g(x)$'s


another pair that have a composition equal to $h(x)$ are;
$$g(x)=x^2\qquad\qquad f(x)=x^{3/2}+1$$

$$f \circ g=f(g(x))=f(x^2)=(x^2)^{3/2}+1=x^3+1=h(x)$$

unklerhaukus · Answer

i am not sure how to find the general solution

anonymous · Answer

Not necessary. Im only required to enter one of the many solutions, the one you gave me works fine. Its the answer i got by myself but i had gotten the functions mixed. Thanx again

unklerhaukus · Answer

cool,