Complete parts ad for the functions fx 4x 2 and gx x2 7

Complete parts (a)-(d) for the functions f(x) = 4x - 2 and g(x) = x^2 - 7. 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) greaterthan g(x). that is. the region below f and above g. Choose the correct graph below.

Solution

the graph of g(x) = x^2 -7 will be open upwards since it is +x^2 a positive sign

and f(x) = 4x -2 it touches x axis when x =2

so graph C) is answer for a)

b). f(x) =g(x)

4x-2 = x^2 -7

x^2 -7 -4x +2=0

x^2 - 4x -5=0

x^2 -5x+x-5=0

x(x-5) +1(x-5) =0

(x-5)(x+1) =0

so x =5 or x=-1

solution set is {-1,5}

for labeling point on f(x)

plug x =-1 and x=5 in f(x) the plot it

f(-1) = 4.-1 -2

=-4 -2

=-6

f(5) = 4.5 -2 = 20 -2

= 18

(-1,-6) and (5,18) polt it on f(x)

similerly find for g(x) and plot those points

d) . otion c) is the answer