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?

d. not one one not onto

Approved

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!

Approved

D
if 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-one
Now its also not onto
definition of onto is for all y belongs to co-domain there should be at least one x in the domain
but in this case for -ve y there is no corresponding value of x
So its neither one one nor onto

Please approve if u are satisfied
Gud Luck :) 

Approved

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 .....

Approved

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 

Approved