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### IIT JEE SOLVED PAPERS ON FUNCTIONS

Here is some solved problems from IIT-JEE previous year papers on functions

Q. [IIT-JEE 2002]Let function f : RR be defined by                     f(x)= 2x + sinx, then f is
(a) one-to-one& onto                    (b) one-to-one but not onto                   (c) onto but not one-to-one            (d) neither one-to-one nor onto
Solution :(a)  Given f(x)= 2x + sinx
On differentiation ,f ′(x)= 2 + cosx ;  as -1 ≤cosx ≤ 1
So, f ′(x) ≥ 0, so f(x) is strictly increasing. Thus f(x) is one-to-one & onto.
Q. [IIT-JEE 2001] Let E = {1,2,3,4} and F = {1,2}. Then the number of onto functions from E to F is
(a) 14   (b) 16    (c) 12    (d) 8
Solution : (a)  Each element of E should have image as 1 or 2.
Thus four elements of E can have images = 24.
Now, for all x E, f(x)=1 or f(x)=2, do not make it as an onto function.
Thus, the total number of onto functions from E to F is = 24 – 2=14.
Q. [IIT-JEE 2000] The domain of definition of the function y(x) given by the equation  2x + 2y = 2 is
(a) 0< x ≤1      (b) 0 x ≤1     (c) -∞< x ≤0     (d) -∞< x <1
Solution :(d)  Given 2y = 2 – 2x  ,
Taking log both sides, ylog2 = log(2 – 2x). Now, 2 – 2x> 0 -∞< x <1.