Question

x + 2For f(x) = 3x - 2 and g(x) =(x+2)/3find the following functions.1a. (fog)(x); b. (gof)(x); c. (fog)(9); d. (gof)(9)

Answer 1

a. (f o g) (x) = x

b. (g o f) (x) = x

c. (f o g) (9) = 9

d. (g o f) (9) = 9

Step-by-step explanation

f(x) = 3x - 2

g(x) = (x + 2)/3

Note that

a) (f o g) (x) means we write f(x) and replace x with g(x)

(f o g) (x) = f[g(x)]

`\begin{gathered} =f\lbrack(x+2)/(3)\rbrack \\ =3((x+2)/(3))-2 \\ =x+2-2 \\ =x \end{gathered}`

b) (g o f) (x) means we write g(x) and replace x with f(x)

(g o f) (x) = g[f(x)]

= g[3x - 2]

`\begin{gathered} =(\lbrack(3x-2)+2\rbrack)/(3) \\ =(3x)/(3) \\ =x \end{gathered}`

c) (f o g) (x) = x

(f o g) (9) = 9

d) (g o f) (x) = x

(g o f) (9) = 9

Hope this Helps!!!