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Question

If the relation f is defined by f(x)={x2,0x33x,3x10
and the relation g is defined by g(x)={x2,0x23x,2x10
then show that f is a function but 'g' is not a function. [5 marks]

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Solution

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)={x2,0x33x,3x10

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)={x2,0x23x,2x10

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]

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