I'm reading Spivak's Calculus, there's a part where he suggests that the student should check some assertions:
$f(x)=x^2$
Then I've evaluated for $f(x+1)$ which is $f(x+1)=(x+1)^2=x^2+2x+1$. Why he says that $f(x+1)=f(x)+2x+1$? Does $f(x)=x^2$ in this case?