Answer:
[tex]f(g(x)) = \frac{10x-9}{3 + 3x}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{x} - 3[/tex]
[tex]g(x) = \frac{3}{x} + 3[/tex]
Required
Find f(g(x))
If: [tex]f(x) = \frac{1}{x} - 3[/tex]
Then:
[tex]f(g(x)) = \frac{1}{3/x + 3} -3[/tex]
Solve the denominator (take LCM)
[tex]f(g(x)) = \frac{1}{\frac{3+3x}{x}} -3[/tex]
[tex]f(g(x)) = \frac{x}{3 + 3x} - 3[/tex]
It can be solved further as:
[tex]f(g(x)) = \frac{x-3(3 + 3x)}{3 + 3x}[/tex]
[tex]f(g(x)) = \frac{x-9 + 9x}{3 + 3x}[/tex]
[tex]f(g(x)) = \frac{10x-9}{3 + 3x}[/tex]
