Answer: (g-f)(x)=-4x
Explanation: According to the graph, line created by function f(x) passes through the points (1,-3) and (0,0) and similarly, line created by the function passes through the points (1,1) and (0,0).
Thus, we can find the equation of the lines with help of formula [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}[/tex] × [tex](x-x_1)[/tex]
so, equation of line created by function f(x)
y+3=[tex]\frac{3-0}{0-1}[/tex]×(x-1)
y+3=[tex]\frac{3}{-1}[/tex]×(x-1)
y+3=-3x+3
y=-3x thus function f(x)=-3x
similarly, equation of line created by function g(x)
y=x thus function g(x)=x
Now, we have to find out, (g-f) (x)= g(x)-f(x)= -3x-x= -4x
