Complete parts ad for the functions fx 6x 1 and gx x2 8

Complete parts (a)-(d) for the functions f(x) = 6x - 1 and g(x) = x^2 - 8. Graph f and g on the same Cartesian plane. Choose the correct graph below. Solve f(x) = g(x). The solution set is. (Use a comma to separate answers as needed.) Use the result of part (b) to label the points of intersection of the graphs of f and g. The points of intersection are (Type an ordered pair. Use a comma to separate answers as needed.) Shade the region for which f(x) > g(x), that is. the region below f and above g. Choose the correct graph below.

Solution

f(x) = 6x -1

g(x) = x^2 -8

g(x) is opening upwards parabola as a=1 >0

point of interesction of f(x) and g(x):

x^2-8 = 6x-1

x^2 -6x -7 =0

x^2 -7x+x-7 =0

(x- 7)(x+1) =0 ----> x= -1 ; x=7

Option B : as f(x) and g(x) intersect at x= 7

b) { -1, 7}

c) Points of intersection are f(-1) = 6(-1) -1 = -7

f(7) = 6*7 -1 = 41

(-1 , -7) and ( 7 , 41)

d) f(x) > g(x)

Region above f(x) is the feasible region

Option: D