The functions f and g are defined by the given equations. f x = 3 + | - 2 x

Question

The functions f and g are defined by the given equations. f x = 3 + | - 2 x - x 2 | g w = | - w w - 1 | - w + 5 If f ( - 4 ) = c , where c is a constant, what is the value of g c ?

Accepted Answer

The correct answer is - 4.9 . The value of f - 4 is the value of f x when x = - 4 . Substituting - 4 for x in the equation f x = 3 + - 2 x - x 2 yields f - 4 = 3 + - 2 - 4 - - 4 2 , or f - 4 = 3 + - 8 , which is equivalent to f - 4 = 3 + 8 , or f - 4 = 11 . Since it's given that f - 4 = c , it follows that c = 11 and the value of g c is the value of g 11 . Substituting 11 for w in the equation g w = - w w - 1 - w + 5 yields g 11 = - 11 11 - 1 - 11 + 5 , or g 11 = - 1.1 - 6 , which is equivalent to g 11 = 1.1 - 6 , or g 11 = - 4.9 . Note that -4.9 and -49/10 are examples of ways to enter a correct answer.

Question c97090