If a discrete signal represented by x[n] = αⁿ u(n), then what is the value of the signal g(n) = x(n) - αx(n - 1)?

Calculation: 

The graph of x[n] = αn u(n),

(α > 0)

⇒ it starts from n=0.

 The graph of αx(n - 1),

⇒ it starts from n = 1.

 g(n) is obtained by subtraction of both graphs.

Hence, 

g(n) = δ(n).

Alternate Method

g(n) = x(n) - αx(n - 1) where (α > 0)

⇒ g(n) = αn u(n) - α*αn-1 u(n-1)

⇒ g(n) = αn u(n) - αn u(n-1)

⇒ g(n) = δ(n).