Question

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 ...?

Answer 1

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) = x² - 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.