For this case we have the following functions:
[tex]f (x) = \frac {1} {x + 5}\\g (x) = x-2[/tex]
We must find f (g (x)). So:
[tex]f (g (x)) = \frac {1} {(x-2) +5} = \frac {1} {x-2 + 5} = \frac {1} {x + 3}[/tex]
Finally we have to:
[tex]f (g (x)) = \frac {1} {x + 3}[/tex]
For the function to be defined the denominator must be different from 0. That is x different from -3.
Answer:
Option B
