Mathematics
# Mathematical Functions

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
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?
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)
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)
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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?
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
get information about a number-theoretic function

Euler phi
do computations with number-theoretic functions

phi(110)
find integral representations for a function

gamma(x) integral representation
sqrt(x) continued fraction