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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)
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