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)

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__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

.

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)

.

__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.