Question 91
Determine all functions $f : \mathbb{R} \to \mathbb{R}$ such that both equations
$$
f(x+1) = 1 + f(x) \text{ and } f(x^4 - x^2) = f(x)^4 - f(x)^2
$$
simultaneously hold for all real $x$. ($\mathbb{R}$ is the set of real numbers.)
$$
f(x+1) = 1 + f(x) \text{ and } f(x^4 - x^2) = f(x)^4 - f(x)^2
$$
simultaneously hold for all real $x$. ($\mathbb{R}$ is the set of real numbers.)