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 of a function 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 representations of a function of a given type:
gamma(x) integral representation
Si(x) limit rep