Even or odd function?

Question

Classify this function as even, odd, or neither and tell me why:

f(x) = x - lxl

Answer 1

A function is even if g(-x) = g(x), is odd if g(-x) = -g(x)

f(-x) = (-x) - |-x| = -x - |x|

which is neither f(x) nor -f(x).

Answer 2

this is neither odd nor even function. you can understand in this way:

if x > 0 => f(x) = 0;

if x< 0 => f(x) = 2x;

which is not either satisfying f(x) = f(-x) nor f(x) = -f(-x);

aliter:
we can understand with the help of graph:

if a function is symmetric with respect to origin then it is odd function and if the function is symmetric with respect to y-axis then it is even function.

the above is neither satisfying anything.

Answer 3

f(2) = 2 - 2 = 0
f(1) = 1 - 1 = 0
f(0) = 0 - 0 = 0
f(-1) = -1 - 1 = -2
f(-2) = -2 - 2 = -4

The function f(x) = 0 for x => 0, f(x) = 2x for x < 0

This function is neither odd nor even.

Answer 4

f(x) = x - lxl

f(-x) = - x - |-x|
= -x - |x|
≠ f(x)
≠ -f(x)

So it is neither odd nor even:

An odd function is one in which f(-x) = - f(x)
An even function is one in which f(-x) = f(x)

This is neither.