Suppose f(t^2+1)=t^4+5t^2+3. What is f(t^2-1)?

Answer 1

f(t^2+1) = t^4+5t^2+3 = (t^2+1)(t^2+4) - 1
= (t^2+1)((t^2+1)+3)-1

That means that f(t) = t(t+3)-1
So,

f(t^2-1) = (t^2-1)((t^2-1)+3)-1 = t^4+t^2-3

Answer 2

Thanks Steve, Could you please explain more on these two last steps:

That means that f(t) = t(t+3)-1
So,

f(t^2-1) = (t^2-1)((t^2-1)+3)-1 = t^4+t^2-3