We need to find out what value we will have to substitute for x
to give t-3, so we set x-2 = t-3 and get
 
    x-2 = t-3
      x = t-1

So we substitute (t-1) for x in 

    f(x-2) = -(x+1)²
f((t-1)-2) = -((t-1)+1)²
  f(t-1-2) = -(t-1+1)²
    f(t-3) = -(t)²
    f(t-3) = -t²

Edwin