# How do you find the inverse of #f(x) = 3log(x-1)#?

I found:

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To find the inverse of (f(x) = 3\log(x - 1)), follow these steps:

- Replace (f(x)) with (y).
- Swap (x) and (y) to interchange the dependent and independent variables.
- Solve the resulting equation for (y).
- Replace (y) with (f^{-1}(x)) to express the inverse function.

Here's how it's done:

- Start with (y = 3\log(x - 1)).
- Swap (x) and (y) to get (x = 3\log(y - 1)).
- Solve for (y):

[x = 3\log(y - 1)]

[x/3 = \log(y - 1)]

[10^{x/3} = y - 1]

[y = 10^{x/3} + 1]

- Replace (y) with (f^{-1}(x)) to express the inverse function:

[f^{-1}(x) = 10^{x/3} + 1]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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