If the relation f is defined by f(x)={x2,0≤x≤33x,3≤x≤10
and the relation g is defined by g(x)={x2,0≤x≤23x,2≤x≤10
then,
'f' is a function and 'g' is not a function
A relation 'R' from 'A' to 'B' is said to be function if every element of 'A' has an unique image in 'B'.
The relation 'f' is given as f(x)={x2,0≤x≤33x,3≤x≤10
The value 3 belongs to both the intervals of f(x).
In the 1st interval: f(3)=32=9
and in 2nd interval: f(3)=3×3=9
Value of f(3) is same in both the intervals, so f(x) is a function.
The relation 'g' is given asg(x)={x2,0≤x≤23x,2≤x≤10
The value 2 belongs to both the intervals of g(x).
In the 1st interval: g(2)=22=4
and in 2nd interval: g(2)=3×2=6
For x=2, g(2) has two values. So g(x) is not a function.
Hence 'f' is a function but 'g' is not a function.