Question

If `f(x)=sqrt(x+1)` and `g(f(x))=1/x`, find `g(2)`?

Answer 1

`g(2)=1/3`

Explanation:

`f(x)=sqrt(x+1)` and `g(f(x))=1/x`

i.e. `g(sqrt(x+1))=1/x`

Let `sqrt(x+1)=t` then `x+1=t^2` and `x=t^2-1`

and `g(sqrt(x+1))=1/xhArrg(t)=1/(t^2-1)`

and `g(2)=1/(2^2-1)=1/3`