Find The Inverse Function from Tables
Questions With Solutions

Find the values of the inverse of a function given by a table? Questions are presented along with detailed Solutions and explanations.


Relationship Between a Function and its Inverse

If f is a function whose inverse is f -1, then the relationship between f and f -1 is written as:

f(a) = b  ⇔  a = f -1(b)


Examples

Use the table below to find the following if possible:
a) f -1(- 4) ,   b) f -1(6) ,   c) f -1(9) ,   d) f -1(10) ,   e) f -1(-10)

function given by table, example

Figure 1. Function given by a table , example 1

Solution

a)
According to the the definition of the inverse function:
a = f -1(- 4)  ⇔  - 4 = f(a) ,
Which means that a is the value of x such f(x) = - 4.
Using the table below for x = 6, f(x) = - 4. Hence a = 6 and therefore f -1(- 4) = 6
b)
a = f -1(6)  ⇔  f(a) = 6
There is no value of x for which f(x) = 6 and therefore f -1(6) is undefined.
c)
a = f -1(9)  ⇔  f(a) = 9
The value of x for which f(x) = 9 is equal to - 4 and therefore f -1(9) = - 4
d)
a = f -1(10)  ⇔  f(a) = 10
There is no value of x for which f(x) = 10 and therefore f -1(10) is undefined.
e)
a = f -1(-10)  ⇔  f(a) = - 10
The value of x for which f(x) = -10 is equal to 8 and therefore f -1(-10) = 8


More Questions with Solutions

Use the table below to find the following if possible:
1) g -1(0) ,   b) g -1(-10) ,   c) g -1(- 5) ,   d) g -1(-7) ,   e) g -1(3)

function given by table.

Solution
a)
According to the the definition of the inverse function:
a = g -1(0)  ⇔  g(a) = 0

Which means that a is the value of x such g(x) = 0 .
Using the table above for x = 11, g(x) = 0 . Hence a = 11 and therefore g -1(0) = 11
b)
a = g - 1(- 5)     if and only if     g(a) = - 5
The value of x for which g(x) = - 5 is equal to 0 and therefore g -1( - 5) = 0
c)
a = g -1(-10)     if and only if     g(a) = - 10
There is no value of x for which g(x) = -10 and therefore g -1(-10) is undefined.
d)
a = g -1(- 7)  ⇔  g(a) = - 7
There is no value of x for which g(x) = - 7 and therefore g -1(- 7) is undefined.
e)
a = g -1(3)   if and only if   g(a) = 3
The value of x for which g(x) = 3 is equal to - 2 and therefore g -1(3) = - 2


More References and links

Find Inverse Function from Graph
Inverse Function
Find Inverse Function (1) - Tutorial
High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers
Middle School Maths (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
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