Let the function f be defined by yfx where x and y are real

Let the function f be defined by y=f(x), where x and y are real numbers. When f(x)=3-x², find f(k²-1).

Solution

f(x) = 3 – x^2

put x = k^2

f(k^2-1) = 3 – (k^2-1)^2

f(k^2-1) = 3 – (k^4 – 2*k^2 +1)

        = 3 – k^4 +2*k^2-1

        = 2 – k^4 +2*k^2