__Example:__ Use the table below to find the following if possible:

a) *f*^{ -1}(- 4) , b) *f*^{ -1}(6) , c) *f*^{ -1}(9) , d) *f*^{ -1}(10) , e) *f*^{ -1}(-10)

.

__Solution__

a) According to the the definition of the inverse function:

a = *f*^{ -1}(- 4) if and only if *- 4 = f(a)* ,

Which means that *a* is the value of *x* such *f(x) = - 4*.

Using the table below for *x = 6, f(x) = - 4*. Hence a = 6 and therefore *f*^{ -1}(- 4) = 6

b) a = *f*^{ -1}(6) if and only if *f(a) = 6*

There is no value of x for which *f(x) = 6* and therefore *f*^{ -1}(6) is undefined.

c) a = *f*^{ -1}(9) if and only if *f(a) = 9*

The value of x for which *f(x) = 9* is equal to - 4 and therefore *f*^{ -1}(9) = - 4

d) a = *f*^{ -1}(10) if and only if *f(a) = 10*

There is no value of x for which *f(x) = 10* and therefore *f*^{ -1}(10) is undefined.

e) a = *f*^{ -1}(-10) if and only if *f(a) = - 10*

The value of x for which *f(x) = -10* is equal to 8 and therefore *f*^{ -1}(-10) = 8
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Answer the following questions

Use the table below to find the following if possible:

a) *g*^{ -1}(0) , b) *g*^{ -1}(-10) , c) *g*^{ -1}(- 5) , d) *g*^{ -1}(-7) , e) *g*^{ -1}(3)

.

(Solutions and explanations are included)