Question

Given: f(x) and g(x) = x+1, what are the restrictions of the domain of f(g(x))

Answer 1

f(g(x)) is obtained replacing x = g(x) into f(x) as follows:

$f(g(x))\text{ = }\frac{1}{x-2+5}=\frac{1}{x+3}$

The domain of a function is the set of all possible values of x.

Given that you can't divide by zero, then

x + 3 ≠ 0

x ≠ 0 - 3

x ≠ -3