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Question

# Which of the following function is an into function if all are defined on f: R → R

A

f(x) = sin(x)

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B

f(x) = cos(x)

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C

f(x) = ex

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D

All of the above

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Solution

## The correct option is D All of the above To check whether a function is an into function or not, we need to consider the co-domain and range of that function. Here, the co –domain for every function is R i.e. all real values. Now let’s check the range of each function. First function is sinx. We know that sinx ranges [-1,1] . So the range < co –domain. And according to the definition of into function, it is an into function. The second function given is cosx. cosx also ranges [-1,1]. So here also the range < co –domain. And the function is into. The third function mentioned is ex , we know that this function ranges from ( 0, ∞). Here also the range < Co – domain. So all the functions given are into functions. The correct options is D.

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