Inverse function: Difference between revisions
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== Relevant observations == | == Relevant observations == | ||
* If g is the inverse function of f, then f is the inverse function of g. | * If '''g''' is the inverse function of '''f''', then '''f''' is the inverse function of '''g'''. | ||
* The domain of f<sup>-1</sup> is the range of f and the range of f<sup>-1</sup> is the domain of f. | * The domain of '''f<sup>-1</sup>''' is the range of '''f''' and the range of '''f<sup>-1</sup>''' is the domain of '''f'''. | ||
* A function may not have an inverse function, but if it has, the inverse function is unique. | * A function may not have an inverse function, but if it has, the inverse function is unique. | ||
Latest revision as of 03:59, 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.