Question

For the given functions f and g find the following and state the domain of each result f(x)=5x+1/4x-7; g(x) = 3x/4x-7

Answer 1

find the following what?
Domain of f and g is all reals except x=7/4

Answer 2

a) (f+g)(x)=
what is the domain of f+g?

b) f/g(x)=
What is the domain of f/g?

Answer 3

since f and g have the same domain, f+g has the same domain as f and g.

f/g = (5x+1)/(3x)
Now, we have to exclude x=7/4 because neither f nor g is defined there.
In addition, we have to exclude x=0 because f/g is not defined there.
So, domain of f/g is all reals except 0,7/4

Answer 4

f+g(x)=?

Answer 5

eh? Just add 'em up:

(f+g)(x)
= f(x)+g(x)
= (5x+1)/(4x-7) + 3x/(4x-7)
= (5x+1+3x)/(4x-7)
= (8x+1)/(4x-7)