f(x) is a function for all real number, is f(x^2) ≤ (f(x))^2 ?
(1) f(x) ≤ 0
(2) If x ≥ 0, f(x) = -x, if x < 0, f(x) = x.
OA is D
(1) f(x) ≤ 0
(2) If x ≥ 0, f(x) = -x, if x < 0, f(x) = x.
OA is D
Hi,
From(1):
f(x) <= 0 irrespective of x being positive or negative
So, f(x^2) <= 0
[f(x)]^2 is square of a real number. It is always non-negative
So, [f(x)]^2 >= 0
So, f(x^2) ≤ (f(x))^2
Sufficient
From(2):
As x^2 ≥ 0 f(x^2) = - x^2 which is never positive
f(x)^2 = x^2 which is non-negative
So, f(x^2) ≤ (f(x))^2
Sufficient
Hence, D
