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If R denotes the set of all real nos. then the function f:R--->R defined f(x)=|x| is
a)one-one only
b)onto only
c)both one-one and onto
d)neither one-one nor onto
choose and explain?
1) Now, for function to be one - one if we draw a horizontal line then it is here will cut the graph at two distinct points. hence it can''t be one-one. it is a many one fn.
2) For onto function it''s range should be equal to the co-daomain given i.e. ''R'' Range of |x| is [0,infinity)
co-domain is not equals to Range.
Thus not an onto fn.
Therefore anr. shuld be ''d)'' neither one-one nor onto.
plz approve!
Dif you draw the graph i.e inverted triangle type with vertex at (0,0)You will find that for one value of y it has two values of x..so definitiely not one-oneNow its also not ontodefinition of onto is for all y belongs to co-domain there should be at least one x in the domainbut in this case for -ve y there is no corresponding value of xSo its neither one one nor ontoPlease approve if u are satisfiedGud Luck :)
it is onto function . for a function to be one - one fuction as the name suggests an element in domain should be mapped with only one element in its range . now in the given question domain is R .
consider |-1| = |1| = 1
since there are more than 1 elements mapped with an element in range it cant be called one one function
for a function to be onto every element in domain should be mapped with atleast one element in range . this is satisified by the function given . so option b .
hope u find it useful .....
The function |x| onlu gives +ve values for any real value u put.
therefore its range is R+
that means it is not onto
Consider two elements in domine i.e., {-1,+1} the value of out put is +1
this means that two elements in domine are mapped to one element in range
which is not one-one
There fore the function is
neither one-one nor onto
please approve it
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