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21 April, 03:51

Which of the following is an even function?

f (x) = |x|

f (x) = x3 - 1

f (x) = - 3x

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Answers (2)
  1. 21 April, 04:11
    0
    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.
  2. 21 April, 04:18
    0
    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.
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