Given two functions as:

f(x) = x2-x-1 and g(x) = 3/x
Find fog(x) also find the domain of f, g and fog

domain of f : any real number

domain of g : any real number except x ≠ 0

fog
= f(g(x))
= f(3/x)
- (3/x)^2 - 3/x - 1

clearly the domain of fog is any real number, except x≠0

last line in calculation should say

= (3/x)^2 - 3/x - 1

To find fog(x), we need to substitute g(x) into f(x).

fog(x) = f(g(x))

First, let's find g(x) by substituting x into the function g(x) = 3/x:

g(x) = 3/x

Next, substitute g(x) back into f(x):

fog(x) = f(g(x)) = f(3/x)

Now, let's find the domain of f, g, and fog:

The domain of a function represents the set of all possible input values (x) for which the function is defined.

For f(x) = x^2 - x - 1, the domain is all real numbers because there are no restrictions on x.

For g(x) = 3/x, the function is undefined when x = 0 because division by zero is not allowed. Therefore, the domain of g(x) is all real numbers except x = 0.

Now, let's find the domain of fog(x) = f(g(x)):

Since g(x) = 3/x, we need to find the values of x that make g(x) defined. As mentioned before, g(x) is undefined when x = 0 because division by zero is not allowed.

Therefore, the domain of fog(x) is all real numbers except x = 0.

In summary:
- The domain of f(x) = x^2 - x - 1 is all real numbers.
- The domain of g(x) = 3/x is all real numbers except x = 0.
- The domain of fog(x) = f(g(x)) is all real numbers except x = 0.