Question

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

What are the restrictions of f(g(x))
A. x=-5
B. x=-3
C. x=2
D.There are no restrictions

Answer 1

For this case we have the following functions:

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

We must find f (g (x)). So:

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

Finally we have to:

`f (g (x)) = \frac {1} {x + 3}`

For the function to be defined the denominator must be different from 0. That is x different from -3.

Answer:

Option B