f(x)=minx,x2∀x∈R then f(x) is

x=x2⇒x−x2=0⇒x=0,x=1fx=x for x 1

f(x)=minx,x2∀x∈R then f(x) is

x=x2⇒x−x2=0⇒x=0,x=1fx=x for x 1

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

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Continuous at 0 , 1

discontinuous at 0

Discontinuous at 1

Continuous on R

answer is C.

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