PLEASE help! I think I have the right answers but I've only got one shot to get it right :((

Question

find and state the domain of each result;

f(x)=2x-7 g(x)=5x+2

 

a.) (f-g)(x)

Would this be -3x-5? the domain being {x such that x is greater than or equal to zero}?

 

b.) (f/g) Is it {x such that x is greater than or equal to zero}???

Answer 1

a) f-g of x is 2x-7-5x-2=-3x-9.

If the domain for f and g separately is all real x, this continues to be the domain for f-g. 

b) f/g of x is (2x-7)/(5x+2) and the domain is restricted because 5x+2 must not be equal to zero, so x cannot equal -0.4 or -2/5, assuming the domain of f and g is all real x.

Answer 2

a) f-g of x is 2x-7-5x-2=-3x-9.

If the domain for f and g separately is x>0, this continues to be the domain for f-g. 

If the domain for f and g separately is all x within the real numbers, the domain remains unchanged for f-g.

b) f/g of x is (2x-7)/(5x+2) and the domain may be restricted because 5x+2 must not be equal to zero, so x cannot equal -0.4 or -2/5. If the domain of g is x>0, then x will never be negative, so the domain continues to be x>0 for f/g. If the domain is all real x then x<>-2/5 for all real values of x except x=-2.5.