Help: find the inverse

Please show work/explanation. Obnoxious and irrelevant answers will be reported.

f(x)=ln(x+3)-2

You switch the x and y variables and then solve for the new y.

f(x) = ln(x + 3) - 2
y = ln(x + 3) - 2
x = ln(y + 3) - 2
x + 2 = ln(y + 3)
e^(x + 2) = y + 3
e^(x + 2) - 3 = y
f^-1(x) = e^(x + 2) - 3 <===ANSWER

f(x)=ln(x+3)-2

step 1: let y=f(x)

y = ln(x+3)-2

step 2: change (swap) all x to y and all y to x

x = ln(y+3)-2

step 3: solve for y

x+2 = ln(y+3)

y+3 = e^(x+2)

y = -3 + e^(x+2)

step 4: let y = f-1(x)

f-1(x) = -3 + e^(x+2) <---- inverse function of x

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y = ln(x+3) - 2

Switch x and y then solve for y.

x = ln(y+3) -2

e^x = e^(ln(y+3) - 2)

e^x = e^(ln(y+3))/e^2

e^x * e^2 = (y+3)

y = e^(x+2) - 3