Find (f•g) (x) when f (x) = sqrt x+3/x and g (x) = sqrt x+3/2x

For multiplying radical expressions, we are first to list down the given.

f (x) = (x + 3/x) ^ (1/2), and

g (x) = (x + 3/2x) ^ (1/2)

We take a look at first the values of the radicands, these are the numbers inside the radical signs. Since, both of the radicands are raised to exponent 1/2, it is easy to say that we just have to multiply them and raise the product to the exponent 1/2 as well. That is,

(f·g) (x) = ((x + 3/x) (x + 3/2x)) ^ (1/2)

Simplifying,

(f·g) (x) = ((x² + 3/2 + 3 + 9/2x²) ^ (1/2))

Further simplification will lead us to the final answer of,

(f·g) (x) = (x² + 9/2 + 9/2x²) ^ (1/2)