FunctionDiscontinuities

Where f fails to be continuous, as a condition in x.

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FunctionDiscontinuities(f, x)the set of real x where f is discontinuous (or undefined).

Typed signatures

Type	Package	Applies
`(expression, symbol) -> expression`	`analytic`	always

Domain: Elementary functions

Details

For every shape this file recognizes, confirmed against wolframscript, Wolfram's discontinuities coincide exactly with FunctionSingularities -- a rational function's poles, Sqrt/Ln's closed excluded region, Tan's Cos(x)==0, none for a polynomial or Exp. This file shares one implementation between the two heads on that basis; it does not attempt the general theory (a removable discontinuity, a jump discontinuity in a piecewise definition) beyond what the classifier already covers.

Examples

Basic #

A pole is a discontinuity

\mathrm{FunctionDiscontinuities}(\frac{1}{x}, x)

Out

x=0

Tangent's poles, where cosine vanishes

\mathrm{FunctionDiscontinuities}(\tan(x), x)

Out

\cos(x)=0

Known value · Wolfram 15.0.0, hand cross-checked

A polynomial is continuous everywhere

\mathrm{FunctionDiscontinuities}(x^2, x)

Out

\mathrm{False}

Scope #

Reported discontinuous for $x\le 0$ , where the real root fails

\mathrm{FunctionDiscontinuities}(\sqrt{x}, x)

Out

x≤0

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