Let f:R⁺→R be a function defined by f(x)=√x.

Determine whether this function is into or onto without using graphical method.

Hi Menka,

A function f: A→B

For this function, domain is A, and Co-domain is B.

If co-domain of the functio is equal to the range, then the function is onto, else it is into.

Here you note that the co-domain is the whole of R.

But f(x) = root(x) can never take negative values. Its range is (0,∞) as domain is R+.

Hence the function is Into.

Also have a look at the solution to the other question on one-one and onto function which you had posted on the forum. There you can get to know how to find the range of functions. (The function there was a combination of a polynomial and a trigonometric function). Also have a look at the previous questions you had posted in the forum on Maths quite a while ago. You can learn some concepts there.

Hope that helps,

All the best,

Regards,

Ashwin (IIT Madras)