state domain if (f-g)(x) f(x)=2x-7; g(x)=5x+2

Question

is -3x-5 right?

{x such that x is greater than or equal to zero}

Answer 1

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

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

Answer 2

Given f(x)=2x-7 and g(x)=5x+2 for (real) x>0.

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.