The relation f is defined by ` f(x) ={(3x+2", "0le x le2),(x^(3)", "2 le x le 5):}.`
The relation g is defined by ` g(x) ={(3x+2", "0le x le1),(x^(3)", "1 le x le 5):}`
Show that f is a function and g is not a function

Explanation

For `0 le x lt 2, f(x) =3x +2 " and for " 2 le x le 10, f(x)=x^(3).`
Now `x=2` appears in both the branches.
From the first branch `f(2)=3(2) +2=8`
From the second branch `f(2)=2^(3)=8`.
Thus, for `x=2`, we have a unique image.
So, given relation is function.
In relation `g(x),x=1` appears in both the branches.
From the first branch `g(1)=3(1)+2=5.`
From the second branch `g(1)=1^(3)=1.`
Thus, element '1' of domain of the relation g corresponds to two different images, viz., 5 and 1.
Hence, this relation is not a function.