The function f and g are defined in the following table Base

The function f and g are defined in the following table. Based on this table, answer the questions below. Is f^-1 a function? Explain why or why not. Is g^-1 a function? Explain why or why not. Evaluate g(f^-1(- 4))

Solution

f^-1 :

The coordinates for finverse are :
(9 , -3)
(2 , -2)
(6 , -1)
(-4 , 0)
(-5 , 1)
(-8 , 2)
(-9 , 3)

All x-values here are different

So, vertical line test is satisfied

So, yes, f inverse is a function

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g inverse has coordinates :
(3,-3)
(0,-2)
(3,-1)
(2,0)
(-3,1)
(-1,2)
(-5,3)

Here, there are 2 x-coordinates that were repeated.

So, this does not satisfy the vertical line test

So, no, g inverse is not a function

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g ( finverse(-4)) :

We have a coordinate (0,-4) in f(x)

So, finverse(-4) = 0

So now, we need g(0)

2

So, the answer is 2