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974 B
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Even and Odd Functions |
Even and Odd Functions
General Functions
A function f
is a mapping from a set A (input/domain) to a set B (output/co-domain).
Even Function:
A function f(x)
is even if and only if f(x) = f(-x)
.
An example of an even function would be f(x) = x^2
because (-x)^2 = x^2
. For example, f(2) = 2^2 = 4 = (-2)^2 = f(-2)
.
The trigonometric functions - cos(x)
and sec(x)
are also even functions
Odd Function
A function f(x)
is odd if and only if f(x) = -f(-x)
An example of an odd function would be f(x) = x^3
because (-x)^3 = -x^3
, so -(-x)^3 = x^3
. For example, f(2) = 2^3 = 8 = -(-8) = -(-2)^3 = -f(-2)
.
The trigonometric functions - sin(x)
, tan(x)
,cot(x)
and cosec(x)
are also odd functions