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

Solution:

We know that,

A function is even if f(x) = f(-x) for all x

1. Given that  f(x) = |x|

The modulus of a function returns the positive value of a function

For example: |-3| = 3 which is similar to even numbers

So f(x) = |x| is an even function.

2. f(x) = x³ - 1

Function with odd powers cannot provide an even function.

i.e., f(-x) = (-x)³ - 1

⇒ -x³ - 1 ≠ f(x)

f(x) = x³ - 1 is not a even function.

3. f(x) = -3x

Function with a negative sign cannot provide an even function.

i.e., f(-x) = -3(-x)

⇒ 3x ≠ f(x)

f(x) = -3x is not a even function.

Therefore, f(x) = |x| is an even function.

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

Summary:

f(x) = |x| is an even function.