Domain of a composition of a function. THANK YOU IN ADVANCE!

Question

Given f(x)= 1/x-4 and g(x)= 1/6-x , find f+g , f-g , fg and f/g. Determine the domain for each function in interval notation.

Answer 1

f(x)= 1/x-4 , g(x)= 1/6-x

f+g= 1/x-4+1/6-x =1/x-x +1/16-4 = 1/x-x-63/16

Domain of f+g is x≠0

x∈(-∞, 0) ∪(0, ∞)

Similar for f-g

fg

= (1/x-4)(1/6-x)=1/(6x)+4x-5/3.. Here Domain D(fg)=is the same as before: = (-∞, 0) ∪(0, ∞)

f/g

= (6(1-4x)/(x(1-6x)), So the domain is

(-∞, 0) ∪(0,1/6) ∪(1/6, ∞)