Let f (x)=1/x and g (x)=x^2+5x. a. find (f×g)(x). b. find the domain and range of (f×g)(x).

we are given

(A)

(f×g)(x)=f(x)*g(x)

now, we can plug it

we can simplify it

(B)

Domain:

Firstly, we will find domain  of f(x) , g(x) and (fxg)(x)

and then we can find common domain

Domain of f(x):

we know that f(x) is undefined at x=0

so, domain will be

∪

Domain of g(x):

Since, it is polynomial

so, it is defined for all real values of x

now, we can find common domain

so, domain will be

∪..............Answer

Range:

Firstly, we will find range of f(x) , g(x) and (fxg)(x)

and then we can find common range

Range of f(x):

we know that range is all possible values of y for which x is defined

since, horizontal asymptote will be at y=0

so, range is

∪

Range of g(x):

Since, it is quadratic equation

so, its range will be

now, we can find common range

so, range will be

∪.............Answer

answer: i think it is (1,-2)