Option D:
Difference between g(x) and f(x) is 44.
Solution:
Let us first write the function of f(x).
Take any two points on the line (0, -1) and (-2, 0).
Here, [tex]x_1=0, y_1=-1, x_2=-2, y_2=0[/tex]
Equation of a line:
[tex]$\frac{y-y_1}{x-x_1} =\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$\frac{y-(-1)}{x-0} =\frac{0-(-1)}{-2-0}[/tex]
[tex]$\frac{y+1}{x} =\frac{1}{-2}[/tex]
Do cross multiplication.
-2(y + 1) = x
-2y - 2 = x
Add 2 on both sides.
-2y = x + 2
Divide by -2 on both sides.
[tex]$y=-\frac{1}{2}x-1[/tex]
y = -0.5x - 1
f(x) = -0.5x - 1
At x = 20,
f(20) = -0.5(20) - 1 = -11
g(x) = 1.5x + 3
g(20) = 1.5(20) + 3 = 33
Difference between g(x) and f(x)
= g(20) - f(20)
= 33 - (-11)
= 33 + 11
= 44
Difference between g(x) and f(x) is 44.
Option D is the correct answer.
