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Q.

Let [t] denotes the (GIF) greatest integer function. Let f(x)=x[x],g(x)=1x+[x] and h(x)=min{f(x),g(x)}  x[2,2] Then h is

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a

continuous  [-2,2] but not differentiable at more than four points.

b

continuous [-2,2]  and  differentiable at  two points.

c

continuous and non- differentiable at four points.

d

None of these.

answer is A.

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Detailed Solution

min{x[x],1x+[x]}h(x)=min{x[x],1(x[x])}

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always continuous in[-2,2] But non differentiable at 7 points.

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Let [t] denotes the (GIF) greatest integer function. Let f(x)=x−[x],g(x)=1−x+[x] and h(x)=min{f(x),g(x)}  x∈[−2,2] Then h is