Question

Given f(x)=1/(x+5) and g(x)=x-2 what are the restrictions of the domain of f(g(x))

Answer 1

domain is

R-{-3}

Explanation:

Given that

`f(x) = (1)/(x+5)`

and
`g(x) = x-2`

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

`f{g(x)}=f(x-2)\\=(1)/(x-2+5) \\=(1)/(x+3)`

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

Hence domain is

R-{-3}

Answer 2

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, +∞)