For f(x)=x/x+1 and g(x)=11/x, find
a. (f of g)(x),
b. the domain of f of g?

Step 1 ：Given the functions \(f(x) = \frac{x}{x + 1}\) and \(g(x) = \frac{11}{x}\), we are asked to find (f of g)(x) and the domain of f of g.

Step 2 ：To find (f of g)(x), we substitute \(g(x)\) into \(f(x)\). This means wherever we see 'x' in the function \(f(x)\), we replace it with the function \(g(x)\).

Step 3 ：Substituting \(g(x)\) into \(f(x)\), we get \(f(g(x)) = \frac{11/x}{(11/x) + 1}\).

Step 4 ：Simplifying the above expression, we get \(f(g(x)) = \frac{11}{x + 11}\).

Step 5 ：Now, we need to find the domain of this function. The function is undefined when the denominator equals zero. So, we need to find the values of x for which \(x + 11 = 0\).

Step 6 ：Solving the equation \(x + 11 = 0\), we get \(x = -11\).

Step 7 ：Therefore, the function is undefined when \(x = -11\). Hence, the domain of the function is all real numbers except -11.

Step 8 ：Final Answer: \(\boxed{f(g(x)) = \frac{11}{x + 11}}\) and the domain of f of g is \(\boxed{x \in \mathbb{R}, x \neq -11}\)