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Question

Which of the following functions are onto functions?

A
f:R[1,1] as f(x)=sin(x)
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B
f:R[1,1] as f(x)=cos(x)
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C
f:R(0,) as f(x)=ex
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D
f:R(,) as f(x)=x3
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Solution

The correct option is D f:R(,) as f(x)=x3

A function f:AB is onto if every element of the co-domain has a pre-image.
i.e., f is onto if range equals co-domain.

We know that the range of the functions sin x and cos x is [-1,1]. Since range equals co-domain, both of these functions are onto.
Similarly, we can check for the other three functions and we’ll find that all functions are onto.


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