The functionis defined by ()=2(+2)2for >−2.

Question

The equation of a curve is such that =().It is given that the point (−1,−1)lies on the curve. Find the equation of the curve.

Answer 1

I have to guess the missing text.

y=f(x)=2a/(x+2)² passes through the point x=-1, y=-1.

Therefore -1=2a/(-1+2)²=2a, a=-½ and f(x)=-1/(x+2)².

Another guess: y=f(x)=2ax/(x+2)².

Plug in (-1,-1):

-1=-2a, a=½, f(x)=1/(x+2)².

Another guess: y=f(x)=ax²/(x+2)².

Plug in (-1,-1):

-1=a, y=-x²/(x+2)².