Question

Find the inverse of each function.
f(x) = log₃ (x+2)

Answer 1

To find the inverse of the function f(x) = log₃ (x+2), switch the roles of x and y and solve for y: y = 3^x - 2.

Step-by-step explanation:

To find the inverse of the function f(x) = log₃ (x+2), we need to switch the roles of x and y and solve for y.

1. Start with the original function: f(x) = log₃ (x+2).

2. Replace f(x) with y: y = log₃ (x+2).

3. Swap x and y: x = log₃ (y+2).

4. Solve for y: Use the exponential form of logarithms by rewriting the equation as 3^x = y+2. Subtract 2 from both sides to isolate y: y = 3^x - 2.

Therefore, the inverse of the function is f⁻¹(x) = 3^x - 2.