Discuss the relation between the concepts of even odd funct

Discuss the relation between the concepts of even & odd functions and the reflection about the coordinate axes. Support your discussion with examples and discuss why even and odd functions are important.

Solution

Even functions :
f(-x) = f(x)

Odd functions :
f(-x) = -f(x)

Even functions when reflected about y-axis will remain the same.

Odd functions when reflected about both the x and y axes will remain the same.

Examples of odd functions :
sinx , tanx , x^3 , x , x^3 + x

Examples of even functions :
cosx, |x| , x^2 , x^4 + x^2 + 1

They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are also very important if we wanna find symmetries of the graph and understand graphs of complex real functions in a simplified manner.