Inverse function: Difference between revisions
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== Definition == | == Definition == | ||
A function g is the inverse function of f if f(g(x))=x for each value of x in the domain of g, and g(f(x))=x for each value of x in the domain of f. The function g is denoted as f<sup>-1</sup> ("inverse of f"). | A function g is the inverse function of f if f(g(x))=x for each value of x in the domain of g, and g(f(x))=x for each value of x in the domain of f. The function g is denoted as f<sup>-1</sup> ("inverse of f"). | ||
=== Notation === | |||
Whereas the notation used for the inverse function resembles the exponencial notation, the superindex -1 has a distinct use. Therefore, in general, f<sup>-1</sup>(x) is not equal to 1/f(x). | |||
Revision as of 23:31, 27 April 2022
An inverse function is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x. Not every function has an inverse.
Definition
A function g is the inverse function of f if f(g(x))=x for each value of x in the domain of g, and g(f(x))=x for each value of x in the domain of f. The function g is denoted as f-1 ("inverse of f").
Notation
Whereas the notation used for the inverse function resembles the exponencial notation, the superindex -1 has a distinct use. Therefore, in general, f-1(x) is not equal to 1/f(x).