Question

Which of the following function is an into function if all are defined on f: R $\to$ R

• A. f(x) = sin(x)
• B. f(x) = cos(x)
• C. f(x) = e^x
• D. All of the above

Answer 1

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 $e^x$ , we know that this function ranges from ( 0, $\infty$). Here also the range < Co – domain. So all the functions given are into functions. The correct options is D.