# Find The Inverse Function Values from Tables

Questions With Detailed Solutions

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

## ExamplesUse 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) .
## Solutiona) 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) = 6 b) a = f if and only if ^{ -1}(6) f(a) = 6There 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) = 9The value of x for which f(x) = 9 is equal to - 4 and therefore f^{ -1}(9) = - 4 d) a = f if and only if ^{ -1}(10) f(a) = 10There is no value of x for which f(x) = 10 and therefore f ^{ -1}(10) is undefined.
e) a = f if and only if ^{ -1}(-10) f(a) = - 10The 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:
g , c) ^{ -1}(-10) g , d) ^{ -1}(- 5) g , e) ^{ -1}(-7) g
^{ -1}(3) . Solutiona) 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) = 11 b) 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) = 0 c) 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^{ -1}(- 7) if and only if g(a) = - 7
There 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

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Find Inverse Function (1) - Tutorial

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