Learn Which Of The Following Is An Odd Function

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# Which of the following is an odd function?

g(x) = x^{2}, g(x) = 5x - 1, g(x) = 3, g(x) = 4x

A function is an odd function if f(-x) = - f(x)

**Example:** x and sinx are odd functions.

A function f(x) is an even function if f(-x) = f(x).

**Example :** x^{2}, cos x are even functions

Given: g(x) = x^{2}

g(-x) = (-x^{2}) = - x × - x = x^{2}

Thus g(x) = x^{2} is an even function as g(x) = g(-x).

g(x) = 5x - 1

g(-x) = 5(- x) - 1 = -5x - 1 = -(5x + 1)

Thus g(x) = 5x - 1 is neither even nor odd

g(x) = 3

g(- x) = 3 is a constant function

g(x) = 4x

g(-x) = 4(-x) = -4x = - g(x)

So the function g(x) = 4x is an odd function.

**Which of the following is an odd function?**

**Summary:**

The function x^{2} is an even function and 4x is an odd function,5x - 1 is neither even nor odd and 3 is a constant function.

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