# Express a Function as the Sum of an Even and an Odd Functions

Tutorials on how to express any function in terms of an even and an odd function are presented with examples in the form of questions including detailed solutions and explanations.

## Questions with Solutions
## Question 1Show that any function f may be expressed as the sum of an even and an odd functions.
Let us write f(x) as follows
## Question 2Express f(x) = 2x^{4} - 5 x^{3} + 2x^{2} + x - 4 as the sum of an even and an odd functions.
f(x) is a polynomial and it is therefore straightforward to separate even and odd parts of the polynomial as follows
## Question 3Express f(x) = 1 / (x - 1) as the sum of an even and an odd functions and check your answer.
In exercise 1, we showed that any function f may be expressed as the sum of an even and an odd functions as follows
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