Functions
Find the domain and range, compose two functions, find an inverse or describe a transformation, with each step written out. Try “find the inverse of f(x) = (2x + 3)/(x − 1)”.
Try an example:
How the Functions works
- For an inverse, replace f(x) with y, swap x and y, then solve for y.
- For a domain, rule out values that divide by zero or give a negative under an even root.
- For a composition f(g(x)), substitute g(x) wherever f has an x.
Frequently asked questions
How do I find the domain of a function?
List every x that is allowed: exclude zeros of denominators and values that make an even-root radicand negative or a log argument non-positive.
How do I know if a function has an inverse?
It must be one-to-one: each output comes from exactly one input (it passes the horizontal line test).
More Algebra calculators
Linear Equation SolverSolve one-variable equations with balancing steps.
Quadratic Equation SolverFactoring, completing the square and the quadratic formula.
System of EquationsSubstitution, elimination and matrix methods.
Inequality SolverLinear, quadratic and absolute-value inequalities with number lines.
Factoring & ExpandingFactor or expand polynomials and expressions.
Polynomial DivisionLong division and synthetic division, remainder theorem.
MathMate can make mistakes. Please double-check important steps and calculations.