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)

function given by its graph .

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

function given by graph solution .



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)

function h given by its graph.

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.

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Updated: 20 January 2017 (A Dendane)
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