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Question

If f(x)=12x1, then on the interval [0,π]

A
tan(f(x)) and 1f(x) are continuous.
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B
tan(f(x)) and 1f(x) are discontinuous.
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C
tan(f(x)) is continuous but 1f(x) is discontinuous.
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D
tan(f(x)) is discontinuous but 1f(x) is continuous.
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Solution

The correct option is C tan(f(x)) is continuous but 1f(x) is discontinuous.
Function is f(x)=12x1 and interval is [0,π].

We know that tan[f(x)]=tan(12x1) is continuous when π2<12x1<π2

π+2<x<π+2 and [0,π](π+2,π+2).

We also know that as 1f(x)=2x2 is not defined when x=2, therefore 1f(x) is not continuous on the interval [0,π]

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