Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)).
y =2/x^(2) + 3

Answer 1

please help :/

Answer 2

one way is that you take g(x)=x^2 and f(x)=2/x + 3.
then y=f(g(x))= f(x^2)= y=2/x^2 + 3

Answer 3

how did you find out what f(x) was and g(x) was?...

Answer 4

it's a very easy technique. just take g(x) to be anything relating to the expression in the equation. for example, in this equation, you can take g(x) to be x^2, 1/x, 1/x^2, etc.
Now, you have choose f(x) accordingly. if you take g(x)=x^2, then you have to take f(x)=2/x + 3; if you take g(x)=1/x, then you have to take f(x)=2x^2+3, and so on.
Hope this helps.

Answer 5

but is that the answer to what f(x) and g(x) are?? or is that just a step to finding what they are...?

Answer 6

there are infinite no. of functions that can work as f and g. there is no one answer.
for example, you take g(x)=2/x^(2) and f(x)=x+3; you can take g(x)=2/x^(2) + 1 and f(x)=x+2, g(x)=2/x^(2)+2 and f(x)=x+1... these all satisfy y=f(g(x)).

Answer 7

thanks so much!!!!! :D