Which of the following is an even function?

f (x) = |x|

f (x) = x3 - 1

f (x) = - 3x

f (x) = |x|

Step-by-step 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.

f (x) = |x|

Step-by-step 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.