HOW TO FIND THE INVERSE OF A GRAPH WITHOUT AN EQUATION

Copy the graphs of the following functions and in each case include the graphs of y = x and y = f ^-1(x):

Problem 1 :

Solution:

Original function is a straight line. So, its inverse graph will also be a straight line.

Step 1 :

Mark some points from the original graph. 

Step 2 :

Exchange the value of x and y. For example, (2, 5) will be converted as (5, 2).

Points from the graph :

(0, 5) ==> (5, 0)

(-2, 0) ==> (0, -2)

Step 3 :

Repeat this for all the point that we have taken from the original graph.

Step 4 :

Joint the point and draw the curve.

Problem 2 :

Solution :

Step 1 :

Mark some points from the original graph. 

Step 2 :

Exchange the value of x and y. 

Points from the graph :

(0, 4) ==> (4, 0)

Step 3 :

Repeat this for all the point that we have taken from the original graph.

Step 4 :

Joint the point and draw the curve.

Problem 3 :

Solution:

Original function is a straight line. So, its inverse graph will also be a straight line.

Step 1 :

Mark some points from the original graph. 

Step 2 :

Exchange the value of x and y. 

Points from the graph :

(0, 1) ==> (1, 0)

(-.3, 0) ==> (0, -3)

Step 3 :

Repeat this for all the point that we have taken from the original graph.

Step 4 :

Joint the point and draw the curve.

Problem 4 :

Solution:

Original function is a exponential graph. So, its inverse also be a exponential graph.

Step 1 :

Mark some points from the original graph. 

Step 2 :

Exchange the value of x and y. 

Points from the graph :

(0, 1) ==> (1, 0)

Step 3 :

Repeat this for all the point that we have taken from the original graph.

Step 4 :

Joint the point and draw the curve.

Problem 5 :

Solution:

Original function is a straight line. So, its inverse also be a straight line.

(2, 0) ==> (0, 2)

(0, 2) ==> (2, 0)

Problem 6 :

Solution:

Original function is a straight line. So, its inverse also be a straight line.

In this graph, point (2, 2) will be converted as (2, 2).