Given f(x) = x-5 and g(x) = Ix+7l, which of the following is the domain of the quotient function f/g?

Question

Given f(x) = x-5 and g(x) = Ix+7l, which of the following is the domain of the quotient function f/g?

a. (-7,oo)

b.(-oo,-7) U (-7,5) U (5,oo)

c. (-7,5) U (5,oo)

d. (-oo,-7) U (-7,oo)

Answer 1

f(x)= x-5, and g(x)= |x+5|. So, this  means that  f/g or f(x)/g(x)= (x-5)/|x+5|

 

So this means that there is a restriction, because division of zero(0) is not allowed. That means the denominator |x+7| cannot be equal to zero. Therefore |x+7|≠0, then by solve the equation you get x+7≠0, therefore x≠7.

 

This means that the quotient of the two functions only have a problem when x=7(x is 7). So the domain in interval notation is (-∞,-7) U (-7,∞).

 

So the answer would be "d."