How to Find the Inverse of a Function Using a Graph
Finding the Inverse of a Function Using a Graph
A function and its inverse function can be plotted on a graph.
If the function is plotted as y = f(x), we can reflect it in the line y = x to plot the inverse function y = f^{−1}(x).
Every point on a function with Cartesian coordinates (x, y) becomes the point (y, x) on the inverse function: the coordinates are swapped around.
How to Find the Inverse of a Function Using a Graph
Finding the inverse of a function using a graph is easy.
Question
Find the inverse function of the function plotted below.
StepbyStep:
1
Plot the function on a graph.
How to Plot a Function
The function is a linear equation and appears as a straight line on a graph.

The constant term gives the yintercept
In our example, the yintercept is 1. The line crosses the yaxis at 1.

The coefficient of the x term gives the slope of the line.
In our example, there is no number written in front of the x. It has an implicit coefficient of 1.
The line has a slope of 1. The line will go up by 1 when it goes across by 1.
2
Plot the line y = x on the same graph.
The line y = x is a 45° line, halfway between the xaxis and the yaxis.
3
Reflect the line y = f(x) in the line y = x.
Each point on the reflected line is the same perpendicular distance from the line y = x as the original line.
The reflected line is the graph of the inverse function.
4
Find the equation of the inverse function.

The yintercept is −1.

The slope is 1.
The equation of the line is:
y = slope x + yintercept
y = 1x + −1
Answer:
The inverse of the function f(x) = x + 1 is:
f^{−1}(x) = x − 1.