Question

Which of the following function is an onto function-

• A. f(x) = sin(x) on f : R $\to$ [-1,1]
• B. f(x) = cos(x) on f : R $\to$ [-1,1]
• C. f(x) = $e^x$ on f : R $\to$ $(0,\infty )$
• D. All of the above.

Answer 1

The correct option is D

All of the above.

One way to check whether a function is into or onto is comparing its co-domain and range. Here the co-domain of each function is given separately. So let’s check each function one by one.

First function given is sinx. The co-domain given for the function is [-1,1]. We know that the range of sinx is [-1,1]. The range and codomain are equal. So the function is onto. Similarly we can check for other two functions and we’ll find that all functions are onto. And the correct option is D.