Table of Domain and Range of Common Functions

A table of domain and range of common and useful functions is presented.
Also a Step by Step Calculator to Find Domain of a Function and a Step by Step Calculator to Find Range of a Function are included in this website.

Algebraic Functions
Function Domain Range
f(x) = x (-? , + ?) (-? , + ?)
f(x) = x 2 (-? , + ?) [0 , + ?)
f(x) = x3 (-? , + ?) (-? , + ?)
f(x) = xn , n even (-? , + ?)[0 , + ?)
f(x) = xn , n odd (-? , + ?) (-? , + ?)
f(x) = | x | (-? , + ?) [0 , + ?)
f(x) = Square root ( x ) [0 , + ?) [0 , + ?)
f(x) = Cube root ( x ) (-? , + ?) (-? , + ?)

Trigonometric Functions
Function Domain Range
f(x) = sin ( x ) (-? , + ?) [-1 , 1]
f(x) = cos ( x ) (-? , + ?) [-1 , 1]
f(x) = tan ( x ) All real numbers except ?/2 + n*? (-in , + ?)
f(x) = sec ( x ) All real numbers except ?/2 + n*? (-? , -1] U [1 , + ?)
f(x) = csc ( x ) All real numbers except n*? (-? , -1] U [1 , + ?)
f(x) = cot ( x ) All real numbers except n*? (-? , + ?)

Inverse Trigonometric Functions
Function Domain Range
f(x) = sin-1( x ) [-1 , 1] [-?/2 , ?/2]
f(x) = cos-1( x ) [-1 , 1] [0 , ?]
f(x) = tan-1( x ) (-? , + ?) (-?/2 , + ?/2)
f(x) = sec-1( x ) (-? , -1] U [1 , + ?) [0 , ?/2) U [? , 3 ?/2)
f(x) = csc-1( x ) (-? , -1] U [1 , + ?) (-? , -?/2] U (0 , ?/2]
f(x) = cot-1( x ) (-? , + ?) (0 , ?)

Logarithmic and Exponential Functions
Function Domain Range
f(x) = a x (-? , + ?) (0 , +?)
f(x) = Log a ( x ) (0 , + ?) (-? , + ?)
f(x) = a x + k , k constant (-? , + ?) (k , + ?)
f(x) = Log a ( x - k) , k constant (k , + ?) (-? , + ?)

Hyperbolic Functions
Function Domain Range
sinh(x) = (e x - e -x) / 2 (-? , + ?) (-? , + ?)
cosh(x) = (e x + e -x) / 2 (-? , + ?) [1 , + ?)
tanh(x) = (e x - e -x) / (e x + e -x) (-? , + ?) (-1 , + 1)
coth(x) = (e x + e -x) / (e x - e -x) (-? , 0) U (0 , + ?) (-? , - 1) U (1 , +?)
sech(x) = 2 / (e x + e -x) (-? , + ?) (0 , 1)
sech(x) = 2 / (e x - e -x) (-? , 0) U (0 , +?) (-? , 0) U (0 , +?)

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