Editing Image (mathematics) (section)

===Image of an element===

If <math>x</math> is a member of <math>X,</math> then the image of <math>x</math> under <math>f,</math> denoted <math>f(x),</math> is the [[Value (mathematics)|value]] of <math>f</math> when applied to <math>x.</math> <math>f(x)</math> is alternatively known as the output of <math>f</math> for argument <math>x.</math> 

Given <math>y,</math> the function <math>f</math> is said to {{em|take the value <math>y</math>}} or {{em|take <math>y</math> as a value}} if there exists some <math>x</math> in the function's domain such that <math>f(x) = y.</math> 
Similarly, given a set <math>S,</math> <math>f</math> is said to {{em|take a value in <math>S</math>}} if there exists {{em|some}} <math>x</math> in the function's domain such that <math>f(x) \in S.</math> 
However, {{em|<math>f</math> takes [all] values in <math>S</math>}} and {{em|<math>f</math> is valued in <math>S</math>}} means that <math>f(x) \in S</math> for {{em|every}} point <math>x</math> in the domain of <math>f</math> .