Question

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

Answer 1

`(f\text{ o g)(x) = }(3x-16)/(17-3x)`

Step-by-step 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)=(2-x)/(x+1) \\ (\text{fog)(x) = }(2-g(x))/(g(x)+1) \end{gathered}`

Recall that

g(x) = 18 - 3x

So,

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

Hope this Helps!!!