The relation f is defined by

f(x) = { x², 0 ≤ x ≤ 3 
3x, 3 < x ≤ 10 }

The relation g is defined by

g(x) = { x², 0 ≤ x ≤ 2 
3x, 2 < x ≤ 10 }

 

For f(x):

At x = 3, both parts give same value: x² = 9 and 3x = 9.

∴ Each x has a unique image, so f is a function.

For g(x):

At x = 2, both parts give different values: x² = 4 and 3x = 6.

∴ x = 2 has two images, so g is not a function.