Wolfram|Alpha Mathematics

Mathematical Functions

Domain & Range ››

compute the domain of a function
domain of f(x) = x/(x^2-1)
compute the range of a function
range of e^(-x^2)
compute domain and range for functions of several variables
domain and range of z = x^2 + y^2

Injectivity & Surjectivity ››

determine whether a given function is injective
is y=x^3+x a one-to-one function?
determine whether a given function is surjective
is x^2-x surjective?

Continuity ››

determine whether a function is continuous
is sin(x-1.1)/(x-1.1)+heaviside(x) continuous
locate discontinuities of a function
discontinuities (x^3+8)/(x^3+3x^2-4x-12)

Periodic Functions ››

compute the period of a periodic function
period y=sin(x)*cos(3x)
find periods of a function of several variables
period sin(x + y^2 - 3z)

Even & Odd Functions

determine whether a function is even or odd
what is the parity of sin(x) is sin(x+pi/4)+cos(x+pi/4) an even function? is f(x,y,z)=sin(xyz) an odd function?

Special Functions ››

compute properties of a special function
zeta(x)
numerically evaluate a special function
sn(2.1, 0.5)
do computations with special functions
d/dx Si(x)^2

Number Theoretic Functions ››

get information about a number-theoretic function
Euler phi
do computations with number-theoretic functions
phi(110)

Representation Formulas ››

find integral representations for a function
gamma(x) integral representation sqrt(x) continued fraction