inverse function
noun1
Mathematics, Sciences For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x.
- Halving is the inverse function of doubling.
- If an inverse function exists for a given function, then it is unique.
4 more examples
- The inverse function of an inverse function is the original function.
- 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).1995, Nicholas M. Karayanakis, Advanced System Modelling and Simulation with Block Diagram Languages, CRC Press, page 217:
- An example of another function that has an inverse function is f(x)#61;4x#43;5. Its inverse is f#123;-1#125;(x)#61;#92;frac#123;x-5#125;#123;4#125;.2014, Mary Jane Sterling, Trigonometry For Dummies, 2nd edition, Wiley, page 51:
- In words, this formula says that the derivative of a function, f, with respect to x, is the reciprocal of the derivative of its inverse function with respect to f.2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147, If f and g are inverse functions, then f'(x)=1/(g'(f(x)))
- Synonyms
- anti-function
- Related terms
- invertible