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:

What you can do with the Functions

Domain, range, composition, inverse and transformations.

Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.

Example input

e.g. find the inverse of f(x) = (2x + 3)/(x - 1)

How the Functions works

  1. For an inverse, replace f(x) with y, swap x and y, then solve for y.
  2. For a domain, rule out values that divide by zero or give a negative under an even root.
  3. 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).

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