To find the inverse of the function f(x) = e^(x −3) + 7, we need to switch x and y and solve for y:
x = e^(y −3) + 7
Subtracting 7 from both sides, we get:
x - 7 = e^(y −3)
Taking the natural logarithm of both sides, we get:
ln(x - 7) = y - 3
Adding 3 to both sides, we get:
ln(x - 7) + 3 = y
Therefore, the inverse of the function f(x) = e^(x −3) + 7 is:
f^(-1)(x) = ln(x - 7) + 3