# Solution to Inverse Function Values from Graphs

The solutions to the grade 11 questions on How to Find Inverse Function Values from Graphs are presented.

 Answer the following questions Question 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) . Solution a) According to the the definition of the inverse function: a = g -1(6)     if and only if     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 -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. Question 2 - Use the graph of function h shown below to find the following if possible: a) h -1(1) , b) h -1(0) , c) h -1(- 1) , d) h -1(2) . Solution a) According to the the definition of the inverse function: a = h -1(1)     if and only if     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) = 0. b) a = h -1(0)     if and only if     h(a) = 0 According to the graph shown, h(π/2) = 0 and therefore h -1(0) = π/2. c) a = h -1(-1)     if and only if     h(a) = -1 According to the graph shown, h(π) = - 1 and therefore h -1(-1) = π. d) a = h -1(2)     if and only if     h(a) = 2 According to the graph shown, there is no value of x for which h(x) = 2 and therefore h -1(2) is undefined.