**Solution:**

To solve this question, we first need to understand the given function and how it is defined.

The function f(x) = 2^x is an exponential function, where the base is 2 and the exponent is x. This means that for any value of x, the function will return the result of raising 2 to the power of x.

Now, let's consider the expression f(x y), which represents the function f applied to the sum of x and y.

To evaluate f(x y), we substitute the value of x + y into the function f(x). Therefore, f(x y) = 2^(x + y).

Now, let's consider the possible options and evaluate each one:

(a) f(x) f(y): This option represents the sum of f(x) and f(y). In this case, we would have f(x) + f(y) = 2^x + 2^y. This is not equivalent to f(x y) = 2^(x + y), so option (a) is not correct.

(b) f(x) . f(y): This option represents the product of f(x) and f(y). In this case, we would have f(x) * f(y) = 2^x * 2^y = 2^(x + y). This is equivalent to f(x y), so option (b) is correct.

(c) f(x) f(y): This option represents the concatenation of f(x) and f(y). Since f(x) and f(y) are both numbers (2 raised to the power of x and y, respectively), it does not make sense to concatenate them. Therefore, option (c) is not correct.

(d) none: This option suggests that none of the above options are correct. However, as we have seen, option (b) is correct.

In conclusion, the correct option is (b) f(x) . f(y), which represents the product of f(x) and f(y).