# 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*, b)

^{ -1}(- 4)*f*, c)

^{ -1}(6)*f*, d)

^{ -1}(9)*f*, e)

^{ -1}(10)*f*

^{ -1}(-10).

## Solution

a) According to the the definition of the inverse function:

*a = f*if and only if

^{ -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) = 6b) a =

*f*if and only if

^{ -1}(6)*f(a) = 6*

There is no value of x for which

*f(x) = 6*and therefore

*f*is undefined.

^{ -1}(6)c) a =

*f*if and only if

^{ -1}(9)*f(a) = 9*

The value of x for which

*f(x) = 9*is equal to - 4 and therefore

*f*

^{ -1}(9) = - 4d) a =

*f*if and only if

^{ -1}(10)*f(a) = 10*

There is no value of x for which

*f(x) = 10*and therefore

*f*is undefined.

^{ -1}(10)e) a =

*f*if and only if

^{ -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*, c)

^{ -1}(-10)*g*, d)

^{ -1}(- 5)*g*, e)

^{ -1}(-7)*g*

^{ -1}(3).

__Solution__

a) According to the the definition of the inverse function:

*a = g*if and only if

^{ -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) = 11b) a =

*g*if and only if

^{ - 1}(- 5)*g(a) = - 5*

The value of x for which

*g(x) = - 5*is equal to 0 and therefore

*g*

^{ -1}( - 5) = 0c) a =

*g*if and only if

^{ -1}(-10)*g(a) = - 10*

There is no value of x for which

*g(x) = -10*and therefore

*g*is undefined.

^{ -1}(-10)d) a =

*g*if and only if

^{ -1}(- 7)*g(a) = - 7*

There is no value of x for which

*g(x) = - 7*and therefore

*g*is undefined.

^{ -1}(- 7)e) a =

*g*if and only if

^{ -1}(3)*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 GraphInverse 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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