Question

Find a formula for the inverse of the function y = e⁽⁶ ⁻ ˣ⁾?

Answer 1

To find the inverse of the function y = e⁽⁶ ⁻ ˣ⁾, swap x and y and solve for y by taking the natural logarithm of both sides.

Step-by-step explanation:

The inverse of the function y = e⁽⁶ ⁻ ˣ⁾ can be found by switching the roles of x and y and then solving for y. Here are the steps to find the inverse:

Start with y = e⁽⁶ ⁻ ˣ⁾

Swap x and y to get x = e⁽⁶ ⁻ y⁾

Solve for y by taking the natural logarithm of both sides: ln(x) = 6 - y

Isolate y by subtracting 6 from both sides: y = 6 - ln(x)

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