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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.

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


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

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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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