Given: g (x) = 1 / x+2 and h (x) 3x

Restrictions on the domain of g0h

All real numbers except for x = - 2/3 (which makes gof undefined)

Step-by-step explanation:

g (x) = 1 / (x+2)

Domain = All real numbers except for x = - 2 (which makes g (x) undefined)

h (x) = 3x

Domain = All real numbers

g (h (x)) = gof

g (h (x)) = gof = 1 / (3x+2)

Where

(3x+2) ≠ 0

x ≠ - 2/3

The new domain of gof is

All real numbers except for x = - 2/3 (which makes gof undefined)