Answer:
1) f(g(x))=x
g(f(x))=x
2) f(x) and g(x) are inverses of each other.
Step-by-step explanation:
The given functions are :
[tex]f(x) = 3x - 2[/tex]
and
[tex]g(x) = \frac{x + 2}{3} [/tex]
1) We want to find:
[tex]f(g(x)) \: and \: g(f(x))[/tex]
This implies that:
[tex]f(g(x)) = f( \frac{x + 2}{3})[/tex]
We substitute into f(x) to get:
[tex]f(g(x)) = 3( \frac{x + 2}{3}) - 2 \\f(g(x)) = x + 2- 2 \\ f(g(x)) = x[/tex]
Also,
[tex]g(f(x)) = g(3x - 2) \\ g(f(x)) = \frac{3x - 2 + 2}{3} \\ g(f(x)) = \frac{3x}{3} \\ g(f(x)) = x[/tex]
2) Since the composition of the two functions:
[tex]f(g(x)) = g(f(x)) = x[/tex]
f(x) and g(x) are inverses of each other.
