__Example:__ Use the graph of *f* shown below to find the following if possible.

a) *f*^{ -1}(5) , b) *f*^{ -1}(0) , c) *f*^{ -1}(- 3) , d) *f*^{ -1}( - 4) , e) *f*^{ -1}(- 5)

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__Solution__

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

*a = f*^{ -1}(5) if and only if *5 = f(a)*

Meaning that *a* is the value of *x* such *f(x) = 5*.

Using the graph below: start from y = 5 on the y-axis and draw a horizontal line to the graph of *f* then go down to the x axis to find *x = 3*. Therefore f(3) = 5. Hence a = 3 and therefore *f*^{ -1}(5) = 3

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b) a = *f*^{ -1}(0) if and only if *f(a) = 0*

According to the graph shown, *f(2) = 0* and therefore *f*^{ -1}(0) = 2.

c) a = *f*^{ -1}(- 3) if and only if *f(a) = - 3*

The value of x for which *f(x) = - 3* is equal to 1 and therefore *f*^{ -1}(- 3) = 1

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

The value of x for which *f(x) = - 4* is 0 and therefore *f*^{ -1}(- 4) = 0.

e) a = *f*^{ -1}(- 5) if and only if *f(a) = - 5*

According to the graph of *f*, there is no value of x for which *f(x) = - 5* and therefore *f*^{ -1}(- 5) is undefined.

Answer the following questions (Detailed Solutions and explanations included)

__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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__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)

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Detailed Solutions and explanations are included