It is found that only f(x) = |x| is even function. so option A is correct answer.
Function is a type of relation, or rule, that maps one input to specific single output.
If we can keep -x in place of x then it does not effect the given function, so it is even function.
i.e. f(-x) = f(x).
also, If we put -x in place of x then the resultant function will get negative of the first function, 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.
Therefore, only f(x) = |x| is even function. so option A is correct answer.
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