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Ans me by using graph
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Asked by ashutoshdsathe2001 | 16 Feb, 2019, 09:44: PM
answered-by-expert Expert Answer
 
Figure shows the function f(x) = x|x| , -1≤ x ≤ 1
 
This function can be rewritten as , f(x) = x2   0≤ x ≤ 1
                                                             = -x2 -1≤ x ≤ 0
 
if f(x1) = x12  and  f(x2) = x22 , if x12 = x22  , then x1 = x2 , x1 begin mathsize 12px style element of end style R  , x1 begin mathsize 12px style element of end style R ,   -1≤ x1 ≤ 1  , -1≤ x2 ≤ 1
hence function is one-one
 
also for every yi = xi2  in set B , we have unique xi in set A  . hence function is also onto
 
Since function is both one-one and onto, function is bijective
Answered by Thiyagarajan K | 18 Feb, 2019, 06:25: PM

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