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If f(x) is discontinuous at only x=1 such that f2(x)=4 ∀x∈R , then the number of points f(x) is discontinuous are [[1]]..

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Detailed Solution

We need to find the number of points in which f(x) is discontinuous.
It is given that f²(x)=4 .
Let us find the root of the above function, i.e
f(x)=±2 ∀x∈R
It is given that the function is continuous everywhere except at x=1 .
So we have the following possibilities:
Firstly, We will look for the points at x≠1
and x=1 ,i.e
f(x) = 2;x≠1
f(x) = −2;x=1
The next possibility can be obtained by switching the values, i.e
f(x)= -2 ;x≠1
f(x) = 2 ;x=1
The third possibility is obtained for the points at x<1 and x≥1, i.ef(x)={2;x<1−2;x≥1
The fourth possibility is obtained by switching the values similar to the second one, i.e
f(x)=−2;x<1
f(x) = 2;x≥1
The fifth possibility is for x>1 and x≤1 ,i.e
f(x)= 2;x>1
f(x) = −2;x≤1
The sixth possibility is obtained similarly as the second and fourth one, i,e
f(x)= −2; x>1
f(x)= 2; x≤1
Thus, the function is discontinuous at 6 points.

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