The table below shows some inputs and outputs of the invertible function fff with domain all real numbers.x | 5 | 3 | 1 | 18 | 0 | 9
f(x) | 9 | -2 | -5 | -1 | 1 | 11
Find the following values:
f^-1 (-2)=
f^-1 (-1)=

Answer: The correct answers are:

- f^{-1}(-2)=3

- f^{-1}(1)=0

Step-by-step explanation:

* Since f^{-1} receives inputs from f's range and maps them to their corresponding elements in f's domain, we can reverse the rows in the table as follows to obtain the inputs and outputs of f^{-1}.

* From this table we see that f^{-1}(-2)=3 and that f^{-1}(1)=0.

* Therefore, the correct answers aref^{-1}(-2)=3 and  f^{-1}(1)=0

The required values f⁻¹(-2) = 3, f⁻¹(-1) = 18, obtained by swapping the input and output values in the inverted table.

To find the inverse of the function,  can swap the input and output values in the given table.

Then, you can use this inverted table to find the values of the inverse function for specific inputs.

As per the table values are,

x     | 5 | 3 | 1 | 18 | 0 | 9

f(x) | 9  | -2 | -5 |-1 | 1 | 11

The values in the inverted table are,

f⁻¹(x)   | 9 | -2 | -5 |-1   | 1   | 11

x       | 5 | 3   | 1  | 18 | 0 | 9

Now, to find the values of the inverse function:

f⁻¹(-2): Looking at the inverted table, when f⁻¹(x) = -2, the corresponding input x is 3. Therefore, f⁻¹(-2) = 3.

f⁻¹(-1): Similarly, when f⁻¹(x) = -1, the corresponding input x is 18. Therefore, f⁻¹(-1) = 18.

Therefore, the values in the inverted table are f⁻¹(-2) = 3 and f⁻¹(-1) = 18 .

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