The two functions have the same output value [tex]y=-1[/tex] when their input value is [tex]x=3[/tex]
Explanation:
The two functions are [tex]f(x)=-\frac{2}{3} x+1[/tex] and [tex]g(x)=\frac{1}{3} x-2[/tex]
To determine the same output value for the two functions, let us substitute the values for x-coordinate(input value) in both the functions.
First, let us substitute the values in the function [tex]f(x)=-\frac{2}{3} x+1[/tex]
For [tex]x=0[/tex] ⇒ [tex]f(0)=1[/tex]
For [tex]x=1[/tex] ⇒ [tex]f(1)=\frac{1}{3}[/tex]
For [tex]x=2[/tex] ⇒ [tex]f(2)=-\frac{1}{3}[/tex]
For [tex]x=3[/tex] ⇒ [tex]f(3)=-1[/tex]
Similarly, let us substitute the values in the function [tex]g(x)=\frac{1}{3} x-2[/tex]
For [tex]x=0[/tex] ⇒ [tex]g(0)=-2[/tex]
For [tex]x=1[/tex] ⇒ [tex]g(1)=-\frac{5}{3}[/tex]
For [tex]x=2[/tex] ⇒ [tex]g(2)=-\frac{4}{3}[/tex]
For [tex]x=3[/tex] ⇒ [tex]g(3)=-1[/tex]
Thus, the two functions have the same output value [tex]y=-1[/tex] when their input value is [tex]x=3[/tex]
