Lets assume your function is:

Given f(x) = {2 if x< -1

................ {-2x if -1 <= x <0

................ {x^2 if x >= 0

(i) 0 is the lower end point of the third part of this function definition, so:

f(0) = 0^2 = 0.

(ii) Since a^2 is always greater than or equal to zero, f(a^2) always uses

the third part of the function definition, so:

f(a^2) = (a^2)^2 = a^4.

RonL