It is observed that for
0≤x≤3, we have f(x)=x2 and for 3≤x≤10, we have f(x)=3x
Also at x=3, f(x)=32=9 or f(x)=3×3=9
i.e., at x=3,f(x)=9
Therefore for every x, 0≤x≤10, we have unique image under f
Thus, the relation f is a function.
Also, the relation g is defined as g(x)={x2,0≤x≤2 3x,2≤x≤10
It can be observed that for x=2, we have g(x)=22=4 and g(x)=3×2=6
Thus, the element 2 of the domain of the relation g has two different images i.e., 4 and 6
Hence, this relation is but not a function.