Odd: -ƒ(x) = ƒ(-x)
Even: ƒ(x) = ƒ(-x)
Examples:
Even: x², x^4, cos x
Odd: sin x, tan x, x, x³.
Try for ƒ(x) = x²
ƒ(-x) = (-x)² = x²
Domain and range:
The [natural] domain of a function is the set of all numbers for which the formula makes sense - that is, the set of all possible inputs.
The range of a function is the set of corresponding outputs - that is, the set of all values of f(x) as x runs through all values in the domain.
Examples:
(a) What is the domain of the function given by g(x) = (3x² - 1)/(x - 2)?
g(x) is an example of a rational function and is define of all values of x except those which makes the denominator equal to zero. The domain of g is therefore {x ∈ R | x =/= 2} or (-∞, 2) U (2, ∞).
(R in this case means all real numbers, just fyi).
I'll do another with range and a harder function:
(b) Find the natural domain and range of f(x) = ln (cos² x)
If f(x) = ln (cos² x) then f has the domain:
{x ∈ R | cos² x > 0} = {x ∈ R| x =/= ±π/2, ±3π/2, ±5π/2...}
Corresponding range is (-∞, 0] as cos² x takes all values in the interval (0, 1].
That took a long time to type out. Hope this helps.