Let f(x) = 3x - 6 and g(x) = x - 2. Find g/f and its domain.

Solution:

Given, f(x) = 3x - 6

g(x) = x - 2

We have to find g/f and its domain.

(g/f)(x) = (x - 2)/(3x - 6)

= (x - 2)/3(x - 2)

= 1/3

To find domain,

When x = 2,

(g/f)(2) = (2 - 2)/3(2 - 2) = 0

The function becomes undefined when x = 2.

Therefore, the domain is the set of all real numbers except 2.

Therefore, (g/f)(x) is 1/3 and its domain is the set of all real numbers except 2.

Let f(x) = 3x - 6 and g(x) = x - 2. Find g/f and its domain.

Summary:

Let f(x) = 3x - 6 and g(x) = x - 2, then g/f is 1/3 and its domain is the set of all real numbers except 2.