One-to-one and inverse functions
Which of the functions is one-to-one?
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An inverse function does exactly the opposite step. If f(x) = 2x + 1 turns 3 into 7, the inverse function f⁻¹ turns 7 back into 3. Only a one-to-one function has an inverse — one that never sends two different numbers to the same value.
What does this generator do?
At the easy level you choose, out of four formulas, the one that is (or is not) one-to-one. At the medium level you find the inverse of a linear function. At the hard level you alternately find the inverse of y = k/(x − m) + n and a point on the graph of f⁻¹.
How to use it
1) One-to-one: if two different x-values give the same y (for example x² for 2 and −2), the function is not one-to-one. 2) Formula of f⁻¹: in the equation y = f(x) swap x and y and make y the subject. 3) Points: if (a, b) lies on the graph of f, then (b, a) lies on the graph of f⁻¹. 4) The graphs of f and f⁻¹ are symmetric about the line y = x.