If f(x)= 1 + ln(x+2), then f^-1 (x)is...?
To find the inverse of the function f(x) = 1 + ln(x + 2), we will follow these steps:
Step 1: Replace f(x) with y:
y = 1 + ln(x + 2)
Step 2: Swap x and y:
x = 1 + ln(y + 2)
Step 3: Solve for y:
x - 1 = ln(y + 2)
Step 4: Rewrite the equation using the properties of logarithms:
e^(x - 1) = y + 2
Step 5: Solve for y by subtracting 2 from both sides:
y = e^(x - 1) - 2
Therefore, the inverse function f^(-1)(x) of f(x) = 1 + ln(x + 2) is f^(-1)(x) = e^(x - 1) - 2.