Question

Which of the following is an even function?
f(x) = |x|
f(x) = x3 – 1
f(x) = –3x

Answer 1

f(x) = |x|

Explanation:

Only f(x) = |x| is an even function. If you evaluate this function at x = 3, for example, the result is 3; if at x = -3, the result is still 3. That's a hallmark of even functions.

Answer 2

f(x) = |x|

Explanation:

If we keep -x in place of x and it does not effect the given function, then it is even function. i.e. f(-x) = f(x).

and, If we put -x in place of x then the resultant function will get negative of the first function, then it is odd function. i.e. f(-x) = -f(x).

1. f(x) = |x|

Put x = -x ,then

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

Hence, f(x) is even function.

2.f(x) = x³ - 1

Put x = -x, then

f(-x) = (-x)³ - 1

= -x³ - 1 = -f(x)

Hence, this function is odd.

3. f(x) = -3x

Put x = -x

then, f(-x) = -3(-x)

= 3x = -f(x)

Hence, the given function is odd function.

Thus, only f(x) = |x| is even function.