Question

# Let $$f(x)=x-\left | x-x^{2} \right |, x\epsilon \left [ -1, 1 \right ]$$. Then the number of points at which $$f(x)$$ is discontinuous is

A
1
B
2
C
0
D
none of these

Solution

## The correct option is A $$0$$case 1:$$x-x^{2}\geq 0 \Rightarrow x\epsilon [0,1]$$$$f(x)=x^{2}$$case 2:$$x-x^{2}\leq 0 \Rightarrow x\epsilon [-1,0)$$$$f(x)= 2x-x^{2}$$At x=0 both the functions tend to zero. So the function f(x) is continuous at x=0.Both the functions are continuous in respective intervals.Hence the number of discontinuous are zero.Mathematics

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