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The number of points at which the function

f(x)=1/log(to the base e)|x| is continuous is

A 1

B 2

C 3

D 4

E infinitely many

Explain.

Correct question is:

The number of points at which the function

f(x)=1/log(to the base e)|x| is discontinuous is:

Solution

$\frac{1}{{\mathrm{log}}_{e}\left|x\right|}isdiscontinuousatx=-1,1,0\phantom{\rule{0ex}{0ex}}As\mathrm{log}0isnotdefinedand\mathrm{log}1=0,so\frac{1}{{\mathrm{log}}_{e}1}isnotdefined.\phantom{\rule{0ex}{0ex}}So\frac{1}{{\mathrm{log}}_{e}\left|x\right|}isdiscontinuousat3points.$

Regards

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