Question

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

Answer 1

Choice D is the answer.

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.

Answer 2

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

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