Question

Given: f(x) = 1/x+5 and g(x) = x - 2.

Answer 1

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

$f(x) = \frac{1}{x+5}$

$g(x) = x - 2$

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

The function is a fraction, which means that the restriction is that the denominator cannot be zero. So

$x - 3 \neq 0$

$x \neq 3$

The restriction of the domain of f(g(x)) is that x cannot be 3.