Question

If f(x)= (1/9)x − 2, what is f⁽⁻¹⁾(x)?

Option 1: f⁽⁻¹⁾(x) = −2x + (1/9)
Option 2: f⁽⁻¹⁾(x) = −(1/9)x + 2
Option 3: f⁽⁻¹⁾(x) = (1/9x + 2
Option 4: f⁽⁻¹⁾(x) = −(1/9)x − 2

Answer 1

The inverse of the function f(x) = (1/9)x - 2 is f⁽⁻¹⁾(x) = 9x + 18.

Step-by-step explanation:

To find the inverse of a function, we need to swap the roles of x and y in the original function and solve for y.

Given f(x) = (1/9)x - 2, we can rewrite it as y = (1/9)x - 2.

To find f⁽⁻¹⁾(x), we swap x and y and solve for y:

x = (1/9)y - 2

Let's solve for y:

x + 2 = (1/9)y

9(x + 2) = y

Thus, f⁽⁻¹⁾(x) = 9x + 18.