`9 - 2e^x = y` Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

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We are asked to determine if the function `y=9-2e^x `   has an inverse function by finding if the function is strictly monotonic on its entire domain using the derivative. The domain is all real numbers.

` y'=-2e^x ` and y'<0 for all real x so the function is monotonic...

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We are asked to determine if the function `y=9-2e^x `   has an inverse function by finding if the function is strictly monotonic on its entire domain using the derivative. The domain is all real numbers.

` y'=-2e^x ` and y'<0 for all real x so the function is monotonic (in this case strictly decreasing) and thus has an inverse function.

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