Consider the following functions:
f(x) = 1 + 1
--
x
g(x) = 1
--
x

Find the following and give the domain of each:
f + g
f - g
f x g
f / g

Domain = ALL REAL NUMBERS - { ? }
( for all )

Question

Consider the following functions:
f(x) = 1 + 1
                 --
                   x
g(x) = 1
           --
            x

Find the following and give the domain of each:
f + g
f - g
f x g
f / g

Domain = ALL REAL NUMBERS - { ? }
     ( for all )

anonymous · Answer

attachment

blacksteel · Answer

I'm assuming your functions are 
$$f = 1 + 1/x,  g = 1/x$$

Then f + g = 1 + 2/x. Since x is in the denominator, the domain must exclude 0 (since division by 0 is undefined). Then f+g has domain R - {0}.

f-g = 1, so the domain is just R.

$$f*g = 1/x + 1/x^2$$ so again we have to exclude any x values that make the denominator 0, in this case x = 0, so the domain is R - {0}.

$$f/g = (1 + 1/x)/(1/x) = (1+1/x)*x = x + 1$$
This again has domain R.

anonymous · Answer

thank you, and thanks for breaking it down too

blacksteel · Answer

Any time!