For Question 17, the function given is:

$f(x) = x^2 - 4x + 24$

To find the inverse of this function, let's follow these steps:

Step 1: Set $y = f(x)$

$y = x^2 - 4x + 24$

Step 2: Solve for $x$ in terms of $y$

First, complete the square to rewrite the quadratic expression: $y = (x^2 - 4x) + 24$

To complete the square, take half of the coefficient of $x$ (which is -4), square it, and add/subtract it inside the equation: $y = (x^2 - 4x + 4 - 4) + 24 = (x - 2)^2 + 20$

Now the equation is: $y = (x - 2)^2 + 20$

Step 3: Isolate the square term

$y - 20 = (x - 2)^2$

Step 4: Take the square root of both sides

$\sqrt{y - 20} = x - 2$

Step 5: Solve for $x$

$x = 2 \pm \sqrt{y - 20}$

Step 6: Swap $x$ and $y$ to express the inverse function

$y = 2 \pm \sqrt{x - 20}$

Thus, the inverse function is: $y = 2 \pm \sqrt{x - 20}$

Conclusion:

Looking at the answer choices, the correct one is:

$y = 2 \pm \sqrt{x - 20}$

This matches the first option.

Would you like further details or clarifications?

Related questions:

1. How do you complete the square for quadratic expressions?
2. What is the method to find the inverse of a function algebraically?
3. Can the inverse of any function be found, and if not, why?
4. How does completing the square help in solving quadratic equations?
5. What is the significance of the square root in the inverse function?

Tip:

Always verify if the original function is one-to-one before solving for the inverse.