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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,


A

'f' is a function and 'g' is not a function

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B

'g' is a function and 'f' is not a function

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C

Both 'f' and 'g' are functions

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D

neither 'f' nor 'g' are functions

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Solution

The correct option is A

'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)={x2,0x33x,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.

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.
Hence 'f' is a function but 'g' is not a function.


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