First slide

Continuity

Question

$f (x) = min \{x, x^{2}\} \forall x \in R then f (x) is$

Moderate

A

discontinuous at 0
B

Discontinuous at 1
C

Continuous on R
D

Continuous at 0 , 1

Solution

$x = x^{2} \Rightarrow x - x^{2} = 0$
$\Rightarrow x = 0, x = 1$
$f (x) = \{\begin{cases} x for x < 0 \\ x^{2} for 0 \leq x \leq 1 \\ x for x > 1 \end{cases}$

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