Answer
[tex](f\text{ o g)(x) = }\frac{3x-16}{17-3x}[/tex]
Explanation
We are given that
f(x) = (2 - x)/(x + 1)
g(x) = 18 - 3x
We are then asked to find (f o g)(x)
(f o g) (x) is the same as writing the expression for f(x) but instead of x, we will write g(x) in the expression.
[tex]\begin{gathered} f(x)=\frac{2-x}{x+1} \\ (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \end{gathered}[/tex]
Recall that
g(x) = 18 - 3x
So,
[tex]\begin{gathered} (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \\ (\text{f o g)(x) = }\frac{2-(18-3x)}{18-3x+1} \\ (f\text{ o g)(x) = }\frac{2-18+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{-16+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{3x-16}{17-3x} \end{gathered}[/tex]
Hope this Helps!!!
