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The function f : ¡ to ¡ defined by f (x)= x |x| will be A. many-to-one and onto B. one-to-one and onto C. many-to-one and into D. one-to-one and into

The function f : ¡ to ¡ defined by f (x)= x |x| will be
A. many-to-one and onto
B. one-to-one and onto
C. many-to-one and into
D. one-to-one and into

Grade:12

4 Answers

Amit
405 Points
5 years ago
Hi there. You can just draw graph and analyse .. For ex. For x0 f(x) will be x². Now try to plot it. It would something of x³ type..graph. Hence it is one one and onto.
Amit
405 Points
5 years ago
For x>0 it will be x² and for x
Samyak Jain
333 Points
5 years ago
f : R\rightarrowR ; f(x) = x |x| 
For x > 0, f(x) = x.x = x2 .
For x = 0, f(x) = 0 .
For x 2 
\therefore The graph of f(x) is always increasing from – infinity to + infinity.
So it is one-one.
Moreover, f(x) covers all the elements of the set of real numbers.
So it is onto.
\therefore f(x) = x |x| is one-one and onto function.
Samyak Jain
333 Points
5 years ago
 
f : R\rightarrowR ; f(x) = x |x| 
For x > 0, f(x) = x.x = x2 .
For x = 0, f(x) = 0 .
For x 2 .
\therefore The graph of f(x) is always increasing from – infinity to + infinity.
So it is one-one.
Moreover, f(x) covers all the elements of the set of real numbers.
So it is onto.
\therefore f(x) = x |x| is one-one and onto function.

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