Question

Find a formula for the inverse of the function y = e^(5 - x).

a) x = 5 - ln(y)
b) x = ln(5 - y)
c) x = 5 - e^y
d) x = ln(e^(5 - y))

Answer 1

The formula for the inverse of the function y = e^(5 - x) is found by swapping x and y and then solving for y, which results in the formula x = 5 - ln(y).

Correct option is a) x = 5 - ln(y)

Step-by-step explanation:

We are looking to find the formula for the inverse of the function y = e^(5 - x). To find the inverse, we swap the variables x and y, which gives us x = e^(5 - y). Then, we solve for y. Isolating y on one side, we get:

y = 5 - ln(x)

Rewriting the final expression back in terms of x, the inverse function is:

x = 5 - ln(y)

This matches with option a) x = 5 - ln(y), which is the correct formula for the inverse of the given function.