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

What restrictions of the domain of f (g (x)) ?

a. x not equal to - 5

b. x not equal to - 3

c. x not equal to 2

d. There are no restrictions

x cannot be - 3 or 2

Step-by-step explanation:

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

= 1 / (x+3)

g (x) cannot have x=2

The domain is restricted where

f (x) has an restriction that x cannot be 5

so g (x) cannot be - 5

-5 = x-2

Add 2 to each side

-5+2 = x

-3