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Question

For the function f(x)=(x21)(9x2)x1,x19,x=1 which of the following statement is correct?

A
f(x) has missing point discontinuity.
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B
f(x) has isolated point discontinuity.
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C
f(x) has finite type discontinuity.
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D
f(x) has infinite type discontinuity.
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Solution

The correct option is B f(x) has isolated point discontinuity.
L.H.L.=limx1(x+1)(x1)(9x2)(x1)
=limx1(x+1)(9x2)=16
R.H.L.=limx1+(x+1)(x1)(9x2)(x1)
=limx1+(x+1)(9x2)=16

And f(1)=9
Here, clearly limit exists but not equal to f(1).
Hence, f(x) has Isolated point discontinuity at x=1.

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