Q. 2 - Calculus

Question

What is the definition of an odd function? An even function?

Step-by-Step Solution

Answer

A function f  is an odd function if $f(-x) = -f\left(x\right)$ for all x in the domain of f.

A function f  is an even function if $f(-x) = f\left(x\right)$ for all x in the domain of f.

Step 1. Explain an odd function.

For a real-valued function $f\left(x\right)$, when the output value of $f(-x)$ is the same as the negative of $f\left(x\right)$, for all values of x in the domain of f, the function is said to be an odd function.

An odd function should hold the following equation $f(-x) = -f\left(x\right)$, for all values of x in the domain of the function f.

Step 2. Explain an even function.

For a real-valued function $f\left(x\right)$, when the output value of $f(-x)$ is the same as $f\left(x\right)$, for all values of x in the domain of f, the function is said to be an even function. An even function should hold the following equation $f(-x) = f\left(x\right)$, for all values of x in the domain of the function f.