Respuesta :

f(x) = 1/(x+5)
g(x)= x-2
f(g(x))= 1/(x-2+5)= 1/(x+3)

Domain of f(g(x)) - all real numbers except x= - 3.
(-∞, - 3)U(-3, +∞)

Answer:

domain is

R-{-3}

Step-by-step explanation:

Given that

[tex]f(x) = \frac{1}{x+5}[/tex]

and[tex]g(x) = x-2[/tex]

We find that domain of f(x) is R-{-5} and g(x) has all real numbers as domain

[tex]f{g(x)}=f(x-2)\\=\frac{1}{x-2+5} \\=\frac{1}{x+3}[/tex]

Thus we find the composition of function has x+3 in denominator

Hence domain is

R-{-3}

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