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. [2 marks]
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. [2 marks]
Hence ′f′ is a function but 'g' is not a function. [1 mark]