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 i would gladly appreciate it

See below.

Step-by-step 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.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction