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EXAMPLE 1

Is the function f(x) = 4x4 + x2 even, odd or neither?

Solution :     f(x) = 4x4 + x2

\ f(-x) = 4(-x)4 + (-x)2

  = 4x4 + x2

  = f (x)

Since f (-x) = f (x), the function is even.

Note : An even degree polynomial function of one variable is always an even function.

EXAMPLE 2

Is the function f(t) = 5t5 - 7t3 - t even, odd or neither?

Solution: f(t) = 5t5 - 7t3 + t

\ f(-t) = 5(-t)5 - 7(-t)3 - (-t)

= -5t5 + 7t3 + t

= - (5t5 - 7t3 -t)

= - f (t)

Since f(-t) = -f (t). The function is odd.

EXAMPLE 3

Find f (t) + f (-t) if f (t) = 3t3 + 2t - 4sin t

Solution : f (t) = 3t3 + 2t - 4 sin t

\ f (-t) = -3t3 - 2t + 4 sin t

\ f (t) + f (-t) = 0

EXAMPLE 4

Find the even and odd components of f(t), defined as,
f(t) =

Index

5. 1 Circular function
5. 2 Periodic function
5. 3 Even & Odd
5.4 Graphs of Trigonometric Functions Supplementary Problems

Chapter 6

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