Real-valued function

A real-valued function has codomain contained in the real numbers.

Table of contents
- Global maximum Real-valued function
- Positive part of a real-valued function Real-valued function

Global maximum

A global maximum of a real-valued function is a value

f (x_{0})

satisfying

f (x) \leq f (x_{0})

throughout its domain.

Positive part of a real-valued function ( $f_{+}$ )

The positive part of a real-valued function

f

is

f_{+} (x) = max (0, f (x))

. Together with the negative part

f_{-} (x) = max (0, - f (x))

, it gives

f = f_{+} - f_{-}

and

∣ f ∣ = f_{+} + f_{-}

.

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Real-valued function by

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A real-valued function is a mathematical function that takes one or more real numbers as input and produces a real number as output.

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