inverse function

English

Noun

inverse function (plural inverse functions)

(mathematics) For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function ${\\displaystyle f:X\\rightarrow Y}$ $\text{[math]}$ , a function ${\\displaystyle g:Y\\rightarrow X}$ $\text{[math]}$ such that, ${\\displaystyle \\forall x\\in X,\\ f(x)=y\\implies g(y)=x}$ $\text{[math]}$ .
Halving is the inverse function of doubling.
If an inverse function exists for a given function, then it is unique.
The inverse function of an inverse function is the original function.
- 1995, Nicholas M. Karayanakis, Advanced System Modelling and Simulation with Block Diagram Languages, CRC Press, page 217,
  In the context of linearization, we recall the reflective property of inverse functions; the ƒ curve contains the point (a,b) if and only if the ƒ^-1 curve contains the point (b,a).
- 2014, Mary Jane Sterling, Trigonometry For Dummies, Wiley, 2nd Edition, page 51,
  An example of another function that has an inverse function is ${\\displaystyle f(x)=4x+5}$ .
  Its inverse is ${\\displaystyle f^{-1}(x)={\\frac {x-5}{4}}}$ .
- 2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147,
  If ${\\displaystyle f}$ and ${\\displaystyle g}$ are inverse functions, then
  ${\\displaystyle f'(x)={\\frac {1}{g'(f(x))}}}$
  In words, this formula says that the derivative of a function, ${\\displaystyle f}$ , with respect to ${\\displaystyle x}$ , is the reciprocal of the derivative of its inverse function with respect to ${\\displaystyle f}$ .