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 === | === Notation === | ||
Revision as of 03:58, 28 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)≠1/f(x).
Relevant observations
- If g is the inverse function of f, then f is the inverse function of g.
- The domain of f-1 is the range of f and the range of f-1 is the domain of f.
- A function may not have an inverse function, but if it has, the inverse function is unique.