Question

Find a formula for the inverse of the function y = e^6 - x.

a) x = e^6 - y
b) x = ln(e^6 - y)
c) x = 6 - ln(y)
d) x = ln(e^6 + y)

Answer 1

The correct formula for the inverse of the function y = e^6 - x is x = ln(e^6 - y)

Step-by-step explanation:

The correct formula for the inverse of the function y = e^6 - x is option b) x = ln(e^6 - y).

To find the inverse of a function, we swap the variables x and y and solve for y. Starting with the given function y = e^6 - x, we swap x and y to get x = e^6 - y. To isolate y, we subtract x from both sides of the equation and take the natural logarithm of both sides, resulting in x = ln(e^6 - y).

Therefore, the correct formula for the inverse of the function y = e^6 - x is x = ln(e^6 - y).