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Question

Consider the following functions:
1. f(x)=x3,xϵR
2. f(x)=sinx,π/2<x<π/2
3. f(x)=ex,xϵR
Which of the above functions have inverse defined on their ranges?

A
1 and 2 only
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B
2 and 3 only
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C
1 and 3 only
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D
1,2 and 3
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Solution

The correct option is B 1 and 2 only
For case (1), Let y=x3x=y13 which is defined on the R range.
For case (2), Let y=sinxx=sin1y which is defined on the (π2,π2) range.
For case (3), Let y=exx=lny which cannot be defined on R as the only inputs it can take are positive.

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