Final answer:
To find the value of f⁻¹(x) when x = 9, we need to solve the equation f(x) = 9 for x. By rearranging the equation and solving the quadratic equation, we find two possible values for x: 9 and 15. Therefore, f⁻¹(9) can be either 9 or 15.
Step-by-step explanation:
To find the value of f⁻¹(x), we need to find the value of x that corresponds to a given value of f(x). In this case, we are given x = 9 and we need to find f⁻¹(9).
First, we need to solve the equation f(x) = 9 for x. The given function f(x) = x² - 24x + 144, so we set it equal to 9:
x² - 24x + 144 = 9
Next, we rearrange the equation to form a quadratic equation:
x² - 24x + 135 = 0
We can now solve this equation to find the values of x. Using factoring or the quadratic formula, we find x = 9 or x = 15.
Since we are looking for the inverse function, f⁻¹(x), we can conclude that f⁻¹(9) = 9 or f⁻¹(9) = 15.