Question

Let f left-parenthesis x right-parenthesis equals 2 x squared plus x minus 3 and g left-parenthesis x right-parenthesis equals x minus 1. Perform the indicated operation, then find the domain. left-parenthesis f minus g right-parenthesis left-parenthesis x right-parenthesis A. x squared minus 4; domain: positive real numbers B. 2 x squared minus 4; domain: all real numbers C. x squared minus 4; domain: all real numbers D. 2 x squared minus 2; domain: all real numbers

Answer 1

Answer:

The option D) is correct

"2 x squared minus 2; domain: all real numbers "

That is $(f-g)(x)=2x^2-2$ and domain is all real numbers

Step-by-step explanation:

Given that the functions f and g are defined by

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

To perform the indicated operation (f-g)(x) and then find the domain :

To find (f-g)(x)

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

Substitute the values of the functions we get

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

$=2x^2+x-3-1(x)-1(-1)$

$=2x^2+x-3-x+1$

$=2x^2-2$ ( by adding the like terms )

Therefore $(f-g)(x)=2x^2-2$ and domain is all real numbers

The option D) is correct

"2 x squared minus 2; domain: all real numbers "

Answer 2

The value of (f-g)(x) is $2x^2-2$. Thus, the correct option is (D)

Two different functions are given that are as follow:

$f(x)=2x^2+x-3$

$g(x)=x-1$

We need to determine the value of the composite function that is (f-g)(x).

Now, by using the property of the composite function (f-g)(x) can also be written as:

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

Substitute the values of both the functions and solve it further for (f-g)(x).

$\begin{aligned}(f-g)(x)&=(2x^2+x-3)-(x-1)\\&=2x^2+x-3-x+1\\&=2x^2-2\\&=2(x^2-1)\end{aligned}$

Thus, the value of (f-g)(x) is $2x^2-2$. Thus, the correct option is (D)

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https://brainly.com/question/5614233