F fprinzo New member Joined Oct 4, 2011 Messages 1 Oct 4, 2011 #1 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,
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,
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Oct 4, 2011 #2 Hello, fprinzo! \(\displaystyle \text{If }\,h(x) \,=\,x^2+2,\) . . \(\displaystyle \text{find }f(x)\text{ and }g(x)\text{ so that: }\:f(g(x))\:=\:h(x).\) Click to expand... 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: .\(\displaystyle \begin{Bmatrix}g(x) &=& x^2 \\ f(x) &=& x+2 \end{Bmatrix}\)
Hello, fprinzo! \(\displaystyle \text{If }\,h(x) \,=\,x^2+2,\) . . \(\displaystyle \text{find }f(x)\text{ and }g(x)\text{ so that: }\:f(g(x))\:=\:h(x).\) Click to expand... 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: .\(\displaystyle \begin{Bmatrix}g(x) &=& x^2 \\ f(x) &=& x+2 \end{Bmatrix}\)
