Question

Let f(x)=(3)/(2x+1)and g(x)=(2)/(x) Findf g AND give its domain.

Answer 1

To find f(g(x)), substitute g(x) into f(x) and simplify. The domain of f(g(x)) is all real numbers except x = -4.

Step-by-step explanation:

To find f(g(x)), we substitute g(x) into f(x) and simplify.

First, substitute g(x) into f(x): f(g(x)) = f(2/x) = (3)/(2(2/x)+1).

Next, simplify the expression: f(g(x)) = (3)/(4/x+1) = (3x)/(4+x).

The domain of f(g(x)) is the set of all values of x that make the expression (4+x) non-zero. Since the function g(x) is defined as g(x) = 2/x, the domain is the set of all real numbers except x = -4.