Question

F(x)=x2-10 and g(x)=11-x find (f-g)(x)(f-g)(10) and (f/g)(x) if they exist

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

​(f​g)(x) ​=

nothing ​(Simplify your ​answer.)

B.

​(f​g)(x) does not exist.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

​(f​g)(​)

nothing ​(Simplify your​ answer.)

B.

The value for ​(f​g)(​) does not exist.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

​(x) ​=

nothing ​(Simplify your ​answer.)

B.

​(x) does not exist.

Click to select and enter your answer(s) and then click Check Answer.

Answer 1

`(f - g)(x) = x^2 + x-21`

`(f - g)(10) = 89`

`(f/g)(x) = (x^2 - 10)/(11 - x)`

Explanation:

Given

`f(x) = x^2 - 10`

`g(x) = 11 - x`

Solving (1): (f-g)(x)

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

Substitute values for f(x) and g(x)

`(f - g)(x) = x^2 - 10 - (11 - x)`

Open Bracket

`(f - g)(x) = x^2 - 10 - 11 + x`

`(f - g)(x) = x^2 -21 + x`

Reorder

`(f - g)(x) = x^2 + x-21`

Solving (2): (f-g)(10)

In (1)

`(f - g)(x) = x^2 + x-21`

So:

`(f - g)(10) = 10^2 + 10-21`

`(f - g)(10) = 100 + 10-21`

`(f - g)(10) = 89`

Solving (3): (f/g)(x)

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

Substitute values for f(x) and g(x)

`(f/g)(x) = (x^2 - 10)/(11 - x)`