If P(x) is a polynomial such that $P\left(x^2+1\right)=\{P(x)\}^2+1$ and P(0) = 0, then P'(0) is equal to
Answer & explanation
Correct answer: option 1
We have,
$P\left(x^2+1\right)=\{P(x)\}^2+1$ for all x
$\Rightarrow P(x)=x$ for all x
Clearly, it also satisfies P(0) = 0
Now,
$P(x)=x \Rightarrow P'(x)=1$ for all $x \Rightarrow P'(0)=1$