Question

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).

show steps please I would gladly appreciate it

Answer 1

See below.

Explanation:

(a) (f - g)(x)

= f(x) - g(x) = 1/x - (x^2 + 5x)

= 1/x - x^2 - 5x.

(b) When x = 0, 1/x is indeterminate so the Domain is All Real except x = 0.

The range is All Real values of (f - g)x except when x = 0.