Respuesta :
Answer:
The restriction of the domain of f(g(x)) is that x cannot be 3.
Step-by-step explanation:
The first step to solve this question is finding the function, replacing the values. So
[tex]f(x) = \frac{1}{x+5}[/tex]
[tex]g(x) = x - 2[/tex]
[tex]f(g(x)) = f(x - 2) = \frac{1}{x - 2 + 5} = \frac{1}{x - 3}[/tex]
The function is a fraction, which means that the restriction is that the denominator cannot be zero. So
[tex]x - 3 \neq 0[/tex]
[tex]x \neq 3[/tex]
The restriction of the domain of f(g(x)) is that x cannot be 3.
