Let f(x)=2x^2+x-3 and g(x)=x-1. perform the indicated operation, then find the domain. (f/g)(x)

The form (f/g)(x) is equal to f(x) divided by g(x). From the equation given by the question, the form (f/g)(x) is just equal to (2x^2+x-3) divided by (x-1).

(f/g)(x) = (2x^2+x-3)/(x-1)
(f/g)(x) = (2x+3)(x-1) / (x-1)
(f/g)(x) = (2x+3)

To get the domain, equate (2x+3) to zero.
2x+3 = 0
x = -(3/2)

So the domain is all set of integers except -(3/2)       

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.