Answer:
The input value is x=1
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
step 1
we have
f(x) passing through the points
(-2,4),(0,2) and (1,1)
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
(0,2) and (1,1)
substitute
[tex]m=\frac{1-2}{1-0}[/tex]
[tex]m=\frac{-1}{1}[/tex]
[tex]m=-1[/tex]
The y-intercept is the point (0,2)
so
[tex]b=2[/tex]
substitute
[tex]f(x)=-x+2[/tex] ----> equation A
step 2
we have
g(x) passing through the points
(-3,-3),(0,0) and (1,1)
Find the slope
This is a linear direct variation, because the line passes through the origin
so
The equation is
[tex]y=kx[/tex]
Find the constant of proportionality k
[tex]k=\frac{y}{x}[/tex]
take the point
(1,1)
substitute
[tex]k=\frac{1}{1}=1[/tex]
substitute
[tex]g(x)=x[/tex] ----> equation B
The solution of the system of equations A and B is the intersection point both graphs
The intersection point is (1,1) -----> given problem
That means----> For an input value of x=1, the output value in both functions is the same
therefore
The input value is x=1
