# Which of the following is an even function?

f(x) = |x|, f(x) = x^{3} - 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) = x^{3} - 1

**Function with odd powers cannot provide an even function.**

i.e., f(-x) = (-x)^{3} - 1

⇒ -x^{3} - 1 ≠ f(x)

**f(x) = x ^{3} - 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.**

## 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.

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