Solutions to Questions on Inverse Function Values from Tables

The solution to the grade 11 questions on Find the Inverse Function Values from Tables are presented.

Answer the following questions


Use the table below to find the following if possible:
a)
g -1(0) , b) g -1(- 5) , c) g -1(-10) , d) g -1(-7) , e) g -1(3)

function given by table.

Solution
a) According to the the definition of the inverse function:
a = g -1(0)     if and only if     g(a) = 0

Which means that
a is the value of x such g(x) = 0.
Using the table above for
x = 11, g(x) = 0. Hence a = 11 and therefore g -1(0) = 11
b) a = g - 1(- 5)     if and only if     g(a) = - 5
The value of x for which
g(x) = - 5 is equal to 0 and therefore g -1( - 5) = 0
c) a = g -1(-10)     if and only if     g(a) = - 10
There is no value of x for which
g(x) = -10 and therefore g -1(-10) is undefined.
d) a = g -1(- 7)     if and only if     g(a) = - 7
There no value of x for which g(x) = - 7 and therefore g -1(- 7) is undefined.
e) a = g -1(3)   if and only if   g(a) = 3
The value of x for which g(x) = 3 is equal to - 2 and therefore g -1(3) = - 2

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