First slide

Continuity

Question

$Let f : R \to R be defined by f (x) = \{\begin{cases} 2 x + 5 if x is irrational \\ 2 x - 7 if x is rational \end{cases} then the number of points$ $of continuity of f (x) for x \in R$

Moderate

Solution

$2 x + 5 and 2 x - 7 cannot be equal for all x \in R$
$∴ f (x) is discontinuous every where$
Number of points of continuity = 0

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