# Find The Inverse Function from Graphs

Questions With Solutions

How to find the values of the inverse of a function from its graph? Grade 11 examples and questions are presented along with their detailed solutions and explanations.

## 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 fb) a = ^{ -1}(5) = 3 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)
## More Questions with SolutionsQuestion 1 - Use the graph of function g shown below to find the following if possible:
a) g , b) ^{ -1}(6) 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) . ## Solutions to the Above Questions
6 = g(a)
Meaning that a is the value of x such g(x) = 6.
Using the graph below for x = 2, g(x) = 6. Hence a = 2 and therefore g
^{ -1}(6) = 2 . b) a = g if and only if ^{ -1}(0) g(a) = 0According to the graph shown, g(- 1) = 0 and therefore g.
^{ -1}(0) = - 1c) a = g if and only if ^{ -1}(- 2) g(a) = - 2The value of x for which g(x) = - 2 is equal to - 2 and therefore g^{ -1}(- 2) = - 2 d) a = g if and only if ^{ -1}(4) g(a) = 4The value of x for which g(x) = 4 is 1 and therefore g.
^{ -1}(4) = 1e) a = g if and only if ^{ -1}(8) g(a) = 8According to the graph of g, there is no value of x for which g(x) = 8 and therefore g is undefined.
^{ -1}(8)
1 = h(a) ,
Meaning that a is the value of x such h(x) = 1.
According to the graph shown, h(0) = 1 and therefore h.
^{ -1}(1) = 0b) a = h if and only if ^{ -1}(0) h(a) = 0
According to the graph shown, h(π/2) = 0 and therefore h.
^{ -1}(0) = π/2c) a = h if and only if ^{ -1}(-1) h(a) = -1
According to the graph shown, h(π) = - 1 and therefore h.
^{ -1}(-1) = πd) a = h if and only if ^{ -1}(2) h(a) = 2
According to the graph shown, there is no value of x for which h(x) = 2 and therefore h is undefined.
^{ -1}(2) |

### More References and links

Find Inverse Function from TableInverse Function

Find Inverse Function (1) - Tutorial

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