Let's begin by finding the inverse of the given function. Then we will graph the function and its inverse.
Finding the Inverse of the Function
Before we can find the of the given function, we need to replace
f(x) with
y.
f(x)=-2x+1⇔y=-2x+1
Now, to algebraically determine the inverse of the given equation, we exchange
x and
y and solve for
y.
Given Equationy=-2x+1 Inverse Equation x=-2y+1
The result of isolating
y in the new equation will be the inverse of the given function.
Finally, we write the inverse of the given equation in function notation by replacing
y with
f-1(x) in our new equation.
f-1(x)=-2x+21
Graphing the Function
Because the given function is a straight line, to draw the graph we should first determine its and .
f(x)=-2x+1
The slope is
-2. The
y-intercept is
1, so the graph crosses the
y-axis at the point
(0,1).
A slope of
-2 means that for every
1 unit we move in the positive horizontal direction, we move
2 units in the negative vertical direction.
slope=-2⇔runrise=1-2
To graph the equation, plot the
y-intercept and then use the slope to find another point on the line.
Graphing the Inverse of the Function
Finally, we can graph the inverse of the function by reflecting the straight line across the line y=x. This means that we should interchange the x and y coordinates of the points that are on the straight line.
Points
|
Reflection across y=x
|
(0,1)
|
(1,0)
|
(1,-1)
|
(-1,1)
|
Let's plot and connect the obtained points.