Answer
a. (f o g) (x) = x
b. (g o f) (x) = x
c. (f o g) (9) = 9
d. (g o f) (9) = 9
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)]
[tex]\begin{gathered} =f\lbrack\frac{x+2}{3}\rbrack \\ =3(\frac{x+2}{3})-2 \\ =x+2-2 \\ =x \end{gathered}[/tex]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]
[tex]\begin{gathered} =\frac{\lbrack(3x-2)+2\rbrack}{3} \\ =\frac{3x}{3} \\ =x \end{gathered}[/tex]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!!!
