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 math questions are presented along with Detailed Solutions and explanations are included.

Example: Use 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)

function given by graph.

Solution
a) 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 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

function given by graph solution.


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.


Answer the following questions (Detailed Solutions and explanations included)

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)

function g given by its graph .

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)

function h given by its graph.

Detailed Solutions and explanations are included

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