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