Question

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

Answer 1

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)