Question

What is the inverse of f (x)=e^x+6

Answer 1

To find the inverse, switch the variables and solve for f(x).

x = e^f(x) + 6
x - 6 = e^f(x)
f(x) = ln(x-6)

hope this helps :)

Answer 2

The inverse means reflect across the x=y line
basically switch x and y and solve for y

steps
replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)

so

f(x)=e^x+6
y=e^x+6
x=e^y+6
minus 6 both sides
x-6=e^y
take the ln of both sides
ln(x-6)=y
y=ln(x-6)
f⁻¹(x)=ln(x-6)