Question

Let f(x) = -20x2 + 14x + 12 and g(x) =5x-6 Find f/g and state its domain a. 5x - 6; all real numbers except x =6/5 b. 5x - 6; all real numbers c. –4x – 2; all real numbers except x =6/5 d. –4x – 2; all real numbers

Answer 1

To find f/g, divide each term in f(x) by g(x). Resulting in f(x)/g(x) = -4x - 2 with the domain being all real numbers except x = 6/5. Hence, the correct answer is c. -4x - 2; all real numbers except x = 6/5.

Step-by-step explanation:

To find the function f/g, we divide the function f(x) by g(x). Given f(x) = -20x2 + 14x + 12 and g(x) = 5x - 6, we divide these to get:

f(x)/g(x) = (-20x2 + 14x + 12) / (5x - 6)

Dividing each term in f(x) by g(x):

f(x)/g(x) = -4x - 2

The domain of this function would be all real numbers except where g(x) = 0, since we cannot divide by zero. g(x) = 0 when x = 6/5. Thus, the domain is all real numbers except x = 6/5.

The correct answer to the student's question is therefore c. -4x - 2; all real numbers except x = 6/5.

Answer 2

In this problem the domain is determined by the denominator alone.  The denom. must NOT be zero.  Thus, set the denom. 5x + 6 = 0 and solve for x.  This x will be the only value that x may not have.  Find the domain of this 5x + 6; your result will also be the domain of the entire given function f/g.