Final answer:
The inverse of the function y = 3e-4x + 1 is f⁻¹(x) = -ln((x - 1)/3) / 4.
Step-by-step explanation:
The inverse of the function y = 3e-4x + 1 can be found by interchanging x and y and solving for the new y. Let's denote the inverse function as f-1(x).
Step 1: Interchange x and y in the original equation.
x = 3e-4f-1(x) + 1
Step 2: Solve for f-1(x).
Subtract 1 from both sides:
x - 1 = 3e-4f-1(x)
Divide both sides by 3:
(x - 1)/3 = e-4f-1(x)
Take the natural logarithm of both sides:
ln((x - 1)/3) = -4f-1(x)
Divide both sides by -4:
f-1(x) = -ln((x - 1)/3) / 4
Therefore, the inverse function is f-1(x) = -ln((x - 1)/3) / 4.