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)

.

__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