Answer: Option B.
Explanation:
A linear function can be written as:
y = a*x + b
where a is the slope and b is the y-intercept.
if the line passes through the points (ax, ay) and (bx, by) then the slope is:
a = (bx - ax)/(by - ay)
In this case, we can see that the line passes through the points:
(1, 3) and (2, 1)
Then the slope is:
a = (1 - 3)/(2 - 1) = -2
y = -2*x + b
In the graph we also can see that the line intersects the y-axis at y = 5, then b = 5.
The line is:
y = f(x) = -2*x + 5.
the inverse function is such that:
g( f(x)) = x
to find the inverse function of a linear equation, we just could isolate x.
y - 5 = -2x
-y/2 + 2.5 = x
Then we could write the inverse function as:
g(x) = - x/2 + 2.5
Now we need to see which pairs belong to this line. I just will evaluate the function g(x) in different values of x, and see which points belong to the line.
g(9) = -9/2 + 2.5 = -4.5 + 2.5 = -2
(9, -2) belongs to the line.
g(7) = -7/2 + 2.5 = -3.5 + 2.5 = -1
Then (7, -1) belongs to this line.
g(5) = -5/2 + 2.5 = 0
Then the point (5, 0) belong to this line.
We can already see that all these points are in option B, then option B is the correct one.