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 of f shown below to find the following,if possible,:a) f^{ 1}(5) , b) f^{ 1}(0) , c) f^{ 1}( 3) , d) f^{ 1}(  4) , e) f^{ 1}( 5)
Solutiona) According to the the definition of the inverse function a = f^{ 1}(5) if and only if 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 yaxis 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^{ 1}(0) if and only if f(a) = 0 According to the graph shown, f(2) = 0 and therefore f^{ 1}(0) = 2. c) a = f^{ 1}( 3) if and only if f(a) =  3 The value of x for which f(x) =  3 is equal to 1 and therefore f^{ 1}( 3) = 1 d) a = f^{ 1}( 4) if and only if f(a) =  4 The value of x for which f(x) =  4 is 0 and therefore f^{ 1}( 4) = 0. e) a = f^{ 1}( 5) if and only if f(a) =  5 According to the graph of f, there is no value of x for which f(x) =  5 and therefore f^{ 1}( 5) is undefined.
More Questions with SolutionsQuestion 1  Use the graph of function g shown below to find the following if possible:a) g^{ 1}(6) , b) g^{ 1}(0) , c) g^{ 1}( 2) , d) g^{ 1}(4) , e) g^{ 1}(8)
Question 2  Use the graph of function h shown below to find the following if possible:
. Solutions to the Above Questions
Solution to Question 1
. b) a = g^{ 1}(0) if and only if g(a) = 0 According to the graph shown, g( 1) = 0 and therefore g^{ 1}(0) =  1. c) a = g^{ 1}( 2) if and only if g(a) =  2 The value of x for which g(x) =  2 is equal to  2 and therefore g^{ 1}( 2) =  2 d) a = g^{ 1}(4) if and only if g(a) = 4 The value of x for which g(x) = 4 is 1 and therefore g^{ 1}(4) = 1. e) a = g^{ 1}(8) if and only if g(a) = 8 According to the graph of g, there is no value of x for which g(x) = 8 and therefore g^{ 1}(8) is undefined.
Solution to Question 2
