To find the inverse of the function y = e^(2-x), we need to follow these steps:

1. Swap x and y: x = e^(2-y)

2. Solve for y:

First, take the natural logarithm (ln) of both sides to get rid of the exponential on the right side:

ln(x) = ln(e^(2-y))

This simplifies to:

ln(x) = 2 - y

3. Solve for y by subtracting 2 from both sides and multiplying by -1:

y = 2 - ln(x)

So, the inverse of the function y = e^(2-x) is y = 2 - ln(x).

Question

To find the inverse of the function y = e^(2-x), we need to follow these steps:

1. Swap x and y: x = e^(2-y)

2. Solve for y:

First, take the natural logarithm (ln) of both sides to get rid of the exponential on the right side:

ln(x) = ln(e^(2-y))

This simplifies to:

ln(x) = 2 - y

3. Solve for y by subtracting 2 from both sides and multiplying by -1:

y = 2 - ln(x)

So, the inverse of the function y = e^(2-x) is y = 2 - ln(x).

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