Question

Given the functions,f(x)= 3x - 2 and g(x) =

Answer 1

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 :

$f(x) = 3x - 2$

and

$g(x) = \frac{x + 2}{3}$

1) We want to find:

$f(g(x)) \: and \: g(f(x))$

This implies that:

$f(g(x)) = f( \frac{x + 2}{3})$

We substitute into f(x) to get:

$f(g(x)) = 3( \frac{x + 2}{3}) - 2 \\f(g(x)) = x + 2- 2 \\ f(g(x)) = x$

Also,

$g(f(x)) = g(3x - 2) \\ g(f(x)) = \frac{3x - 2 + 2}{3} \\ g(f(x)) = \frac{3x}{3} \\ g(f(x)) = x$

2) Since the composition of the two functions:

$f(g(x)) = g(f(x)) = x$

f(x) and g(x) are inverses of each other.