Question

Use the given functions to find f (g(x)), and give the restrictions on x.

F(x)= 1/x-3 and g(x) = 3/x +3

F(g(x)) = ?

Where x(doesn’t = ?

Answer 1

`f(g(x)) = (10x-9)/(3 + 3x)`

Explanation:

Given

`f(x) = (1)/(x) - 3`

`g(x) = (3)/(x) + 3`

Required

Find f(g(x))

If:
`f(x) = (1)/(x) - 3`

Then:

`f(g(x)) = (1)/(3/x + 3) -3`

Solve the denominator (take LCM)

`f(g(x)) = (1)/((3+3x)/(x)) -3`

`f(g(x)) = (x)/(3 + 3x) - 3`

It can be solved further as:

`f(g(x)) = (x-3(3 + 3x))/(3 + 3x)`

`f(g(x)) = (x-9 + 9x)/(3 + 3x)`

`f(g(x)) = (10x-9)/(3 + 3x)`