Question

2 - 2f(x)X + 1g(x) = 18 - 3.2Escreva (fog)(2) como uma expressão em função de 2.(fog)(x) =

Answer 1

Answer

$(f\text{ o g)(x) = }\frac{3x-16}{17-3x}$

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.

$\begin{gathered} f(x)=\frac{2-x}{x+1} \\ (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \end{gathered}$

Recall that

g(x) = 18 - 3x

So,

$\begin{gathered} (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \\ (\text{f o g)(x) = }\frac{2-(18-3x)}{18-3x+1} \\ (f\text{ o g)(x) = }\frac{2-18+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{-16+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{3x-16}{17-3x} \end{gathered}$

Hope this Helps!!!