# Find The Inverse Function Values from Tables Questions With Detailed Solutions

How to find the values of the inverse of a functions given by tables? Grade 11 maths questions are presented along with Detailed Solutions and explanations are included.

## 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)

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## Solution

a) According to the the definition of the inverse function:
a = f -1(- 4)     if and only if     - 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)     if and only if     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)     if and only if     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)     if and only if     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)     if and only if     f(a) = - 10
The value of x for which f(x) = -10 is equal to 8 and therefore f -1(-10) = 8

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

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(Solutions and explanations are included)