To find the inverse of y = 3e^(4x+1), you would have to change the variables and solve for the y
1) Replace x with y and y with x
2) Solve the equation (x and y swap from step 1 applied) for y
3) Replace the y for f^—1 (x)
Applying that process, we are interchanging the variables x and y
Solve: x = 3e^4y+1 for: y
3e^4y+1 —> x
(3e^4y+1)/3 —> x/3
If f (x) = g (x), then 1n (f(x)) = 1n (g(x))
1n (e^4y+1) = 1n (x/3)
Apply log rule: logA(x^b) = b x logA (x)
(4y + 1) 1n (e) = 1n (x/3)
4y + 1 = 1n (x/3)
y = (1n(x/3)-1)/4
f^—1 (x) = (1n(x/3)-1)/4
The inverse of the function 3e^4y+1 is f^—1 (x) = (1n(x/3)-1)/4
