Inverse of Strictly Monotone Continuous Real Function is Strictly Monotone and Continuous/Examples/Arbitrary Example 1
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Example of Use of Inverse of Strictly Monotone Continuous Real Function is Strictly Monotone and Continuous
Consider the real function:
- $\forall x \in \closedint 0 1: \map f x = y = 2 x + 3$
This has an inverse:
- $\map {f^{-1} } y = x = \dfrac {y - 3} 2$
on the closed interval $\closedint 3 5$
Hence we can say:
- $f: x \mapsto 2 x + 3$ on $\closedint 0 1$
and:
- $f^{-1}: x \mapsto \dfrac {x - 3} 2$ on $\closedint 3 5$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inverse: 1. (of a function)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inverse: 1. (of a function)