If functions math xmlns=http://www.w3.org/1998/Math/MathMLmif/mimo(/momi mathvariant=normal...
If functions math xmlns=http://www.w3.org/1998/Math/MathMLmif/mimo(/momi mathvariant=normalx/mimo)/mo/math and math xmlns=http://www.w3.org/1998/Math/MathMLmi mathvariant=normalg/mimo(/momi mathvariant=normalx/mimo)/mo/math are defined on math xmlns=http://www.w3.org/1998/Math/MathMLmi mathvariant=normalℝ/mimo→/momi mathvariant=normalℝ/mi/math such that math xmlns=http://www.w3.org/1998/Math/MathMLmif/mimo(/momi mathvariant=normalx/mimo)/momo=/momfenced open={ close=mtablemtrmtdmi mathvariant=normalx/mimo+/momn3/mnmo,/mo/mtdmtdmi mathvariant=normalx/mimo∈/momtext rational /mtext/mtd/mtrmtrmtdmn4/mnmi mathvariant=normalx/mimo,/mo/mtdmtdmi mathvariant=normalx/mimo∈/momtext irrational /mtext/mtd/mtr/mtable/mfenced/math,
\( \mathrm{g}(\mathrm{x})=\left\{\begin{array}{cc}\mathrm{x}+\sqrt{5} & , \quad \mathrm{x} \in \text { irrational } \\ -\mathrm{x} & , \quad \mathrm{x} \in \text { rational }\end{array}\right. \) then \( (f-\mathrm{g})(\mathrm{x}) \) is-
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