function problem

[fprinzo]

here is my problem.

if h(x)=x^2+2, howdo I find f(x) and g(x) so that f(g(x))=h(x) ???

your help is appreciated,

 

[soroban]

Hello, fprinzo!

\(\displaystyle \text{If }\,h(x) \,=\,x^2+2,\)

. . \(\displaystyle \text{find }f(x)\text{ and }g(x)\text{ so that: }\:f(g(x))\:=\:h(x).\)

I'll solve this the "obvious way",
. . but JeffM is correct; there is an infinite number of solutions.


\(\displaystyle \text{Examine }h(x) \,=\,x^2+2\)

There are two ordered commands:
. . (1) square \(\displaystyle x\)
. . (2) add 2

We can let: .\(\displaystyle \begin{Bmatrix}g(x) &=& x^2 \\ f(x) &=& x+2 \end{Bmatrix}\)