What is the inverse of the function y=3e^(4x+1)

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

b) well because you get well

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