Let f (x) = x2 - 81. Find f-1 (x).

Question 7 options:

1) ± √x+81

2) ± 9√x

3) 1 over x^2-81

4) x^2 over 81 ... ?

The answer is 1) ± √x+81

Step 1: Substitute y for f (x).

Step 2: Since every (x, y) has its partner (y, x) y switch x and y.

Step 3: Solve for y.

Step 1.

The function is: f (x) = x ² - 81

Substitute y for f (x) : y = x² - 81

Step 2.

Switch x and y: x = y² - 81

Step 3.

Solve for y (which is now f⁻¹ (x)) : f⁻¹ (x) = y

x = y² - 81

y² = x + 81

y = + - √ (x+81)

Therefore, the choice 1) is correct.