# Find The Inverse Function Values from Graphs

Questions With Detailed Solutions

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

## ExampleUse the graph off shown below to find the following,if possible,:
a) f , b) ^{ -1}(5)f , c) ^{ -1}(0) f , d) ^{ -1}(- 3) f , e) ^{ -1}( - 4) f^{ -1}(- 5) .
## Solutiona) According to the the definition of the inverse function a = f if and only if ^{ -1}(5)5 = f(a)Meaning that a is the value of x such f(x) = 5.
Using the graph below: start from y = 5 on the y-axis and draw a horizontal line to the graph of f then go down to the x axis to find x = 3. Therefore f(3) = 5. Hence a = 3 and therefore f^{ -1}(5) = 3 . b) a = f if and only if ^{ -1}(0) f(a) = 0According to the graph shown, f(2) = 0 and therefore f.
^{ -1}(0) = 2c) a = f if and only if ^{ -1}(- 3) f(a) = - 3The value of x for which f(x) = - 3 is equal to 1 and therefore f^{ -1}(- 3) = 1 d) a = f if and only if ^{ -1}(- 4) f(a) = - 4The value of x for which f(x) = - 4 is 0 and therefore f.
^{ -1}(- 4) = 0e) a = f if and only if ^{ -1}(- 5) f(a) = - 5According to the graph of f, there is no value of x for which f(x) = - 5 and therefore f is undefined.
^{ -1}(- 5)
## Answer the following questions(Detailed Solutions and explanations included)
g , c) ^{ -1}(0) g , d) ^{ -1}(- 2) g , e) ^{ -1}(4) g
^{ -1}(8) .
h , c) ^{ -1}(0) h , d) ^{ -1}(- 1) h
^{ -1}(2) . Detailed Solutions and explanations are included |

### More References and links

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