0791616e85
Fixed copy/pasting(?) typos, also changed the 'because' in each example to explain the why instead of just showing it's true for a single number, not mentioning any others. (Proof by example is very, very, VERY bad to encourage.)
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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