For the given functions f and g find the following and state

For the given functions f and g, find the following and state the domain of each result. f(x) = 2x - 5; g(x) = 7x + 2 (a) (f - g)(x) = What is the domain of f - g? {x|x notequalto 5/2} {x|x > 5/2} {x|x Greaterthanorequalto 0} {x|x is any real number} (b) (f/g)(x) = What is the domain of f/g? {x|x Greaterthanorequalto 0} {x|x > -2/7} {x|x notequlato -2/7} {x|x is any real number}

Solution

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

a)(f-g)(x)=f(x)-g(x)

=2x-5 -7x-2

=-5x-7

domain is {x|x is any rewal number}

b)(f/g)(x)

=f(x)/g(x)

=(2x-5)/(7x+2)

(f/g)(x) is undefined qhen g(x)=0

7x+2=0

x=-2/7

domain is {x|x-2/7}