Question

The table below shows some inputs and outputs of the invertible function f with a domain of all real numbers:

x: 9, -11, 7, 11, -6, -13
f(x): 11, 4, -6, -1, -15, -5

Find the Following Values:

Find f⁽⁻¹⁾⁽⁻¹⁵⁾.
Find f⁽⁻¹⁾⁽⁴⁾ ⁼ f(9)

Answer 1

To determine f⁻¹(-15) we find the input that gives an output of -15, which is -6. Similarly, f⁻¹(4) is the input that results in an output of 4, which is -11. These inverse function values are determined from the given input-output pairs of the function f.

Step-by-step explanation:

To find the value of f⁻¹(-15), we look at the outputs of the function f given in the table and identify which input x corresponds to the output of -15. In this case, we see that f(-6) = -15, hence f⁻¹(-15) = -6.

For the value f⁻¹(4), we need to find the input x for which f(x) is 4. According to the table, f(-11) = 4, so f⁻¹(4) = -11. It is also given that f(9) = 11, but since we are looking for the value of f⁻¹(4), the appropriate comparison is between f⁻¹(4) and the input value for f which is 9. Since finding f(9) isn't directly related to calculating f⁻¹(4) in this problem, the comparison f⁻¹(4) = f(9) does not hold true. Instead, the correct comparison would be f⁻¹(4) = -11.