Question

Let f and g be functions. (a) The function (f + g)(x) is defined for all values of x that are in the domain(s) of ____________. (b) The function (fg)(x) is defined for all values of x that are in the domain(s) of __________. (c) The function (f/g)(x) is defined for all values of x that are in the domain(s) of__________

Answer 1

a) for all values of x that are in the domains of f and g.

b) for all values of x that are in the domains of f and g.

c) for all values of x that are in the domains of f and g with g(x)≠0

Explanation:

a) By definition (f+g)(x)=f(x)+g(x). Then x must be in the domain of f and g.

b) By definition (fg)(x)=f(x)g(x). Then x must be in the domain of f and g.

c) By definition (f/g)(x)=f(x)/g(x). Then x must be in the domain of f and g and g(x) must be different of 0.