Question

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

Answer 1

To find (f/g)(x), divide f(x) by g(x). In this case,
`f(x) = 2x^2+x-3` and g(x) = x-1. Simplifying the expression, we get (f/g)(x) = 2x + 3. The domain is all real numbers except x = 1.

Step-by-step explanation:

To find the operation (f/g)(x), we need to divide the function f(x) by g(x).

Given
`f(x) = 2x^2+x-3` and g(x) = x-1:

(f/g)(x) = f(x) / g(x)

Substitute the given functions:

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

Now we need to simplify the expression:

Using polynomial division or long division, divide
`2x^2+x-3` by x-1 to get:

(f/g)(x) = 2x + 3

The domain of the function (f/g)(x) is all real numbers except x = 1, since division by zero is undefined.

Answer 2

2x+3; domain: all real numbers except x=1