# 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.

## 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)

.

## 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

## 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) .

Solution
a) According to the the definition of the inverse function:
a = g -1(0)     if and only if     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)     if and only if     g(a) = - 7
There 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