Question

If f(x) = 1/x-8 and g(x) square root of x-2, what is (f of g) (x) and what is the domain?

Answer 1

The composition (f of g) (x) is found by substituting g(x) into f(x), leading to f(g(x)) = 1/(sqrt(x-2) - 8). The domain of the function is all x greater than or equal to 2, excluding any x where sqrt(x-2) - 8 equals zero.

Step-by-step explanation:

The student is asking about function composition and domain in the subject of mathematics. First, we identify the functions: f(x) = 1/(x-8) and g(x) = √(x-2). The composition (f of g) (x) is found by substituting g(x) into f(x). The steps would be as follows:

1. 
   
3. Find g(x), which is √(x-2).
4. 
   
6. Substitute g(x) into f(x) to get f(g(x)) = 1/(√(x-2) - 8).
7. 
   
9. Simplify the expression if possible.

Regarding the domain, it must be determined for both g(x) and f(g(x)). The domain of g(x) = √(x-2) is x ≥ 2, because square roots cannot be negative. For f(g(x)), we have to exclude any x where √(x-2) - 8 = 0 to prevent division by zero, which further restricts the domain.