Question

Which expression is equal to (f + g)(x)?

Answer 1

B.

Explanation:

`= f(x) + g(x)\\= \sqrt{x^(2) +28x+196} +x^(3) -729\\factor (x^(2) +28x+196) to ((x+14)^(2))\\= \sqrt{(x+14)^(2) } +x^(3) -729\\= x+14+x^(3) -729\\=x^(3) +x-715`

Answer 2

B.

`(f + g)(x) = {x}^(3) + x- 715`

EXPLANATION

The given functions are:

`f(x) = \sqrt{ {x}^(2) + 28x + 196}`

This is the same as

`f(x) = \sqrt{ {(x + 14)}^(2) }`

`f(x) = x + 14`

and

`g(x) = {x}^(3) - 729`

`(f + g)(x) = f(x) + g(x)`

`(f + g)(x) = x + 14 + {x}^(3) - 729`

`(f + g)(x) = {x}^(3) + x- 715`

The correct answer is B