First slide

Continuity

Question

The set of points of continuity when $f (x) = {\begin{matrix} 1 & if & x is rational \\ - 1 & if & x is irrational \end{matrix}$

Moderate

A

$R$
B

$φ$
C

$(- 1, 1)$
D

$R^{+}$

Solution

$f (x) = {\begin{matrix} 1 & if & x is rational \\ - 1 & if & x is irrational \end{matrix}$
between two rational numbers there are infinite irrational numbers and
between two irrational numbers there are infinite rational numbers.
Clearly $f (x)$ is discontinuous every where
Set of points of continuous $= ϕ$

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