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

A) x^2-4; domain: all positive real numbers

B) 2x^2-4; domain: all real numbers

C) x^2; domain: all real numbers

D) 2x^2-2; domain: all real numbers

The answer is (D) ⇒ 2x² - 2; domain: all real numbers

Step-by-step explanation:

∵ f (x) = 2x² + x - 3

∵ g (x) = x - 1

∴ (f - g) (x) = 2x² + x - 3 - (x - 1) = 2x² + x - 3 - x + 1

= 2x² - 2

∵ There is no value of x make the function undefined

∴ The domain is all real numbers

Choice D is the answer.

Step-by-step explanation:

We have given two functions.

f (x) = 2x²+x-3 and g (x) = x-1

We have to find (f-g) (x) and we have to find the domain of (f-g) (x).

The formula to find the

(f-g) (x) = f (x) - g (x)

Putting values in above formula, we have

(f-g) (x) = (2x²+x-3) - (x-1)

(f-g) (x) = 2x²+x-3-x+1

Adding like terms, we have

(f-g) (x) = 2x²-2

The domain is set of all input values.

Hence, domain of (f-g) (x) is all real numbers.