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

Answer 1

Cora Alexander

#y=log^(-1)(x/3)+1#

Write as #y=3log(x-1)#

Manipulate to give:

#log(x-1)=y/3#

#log^(-1)(x-1)=log^(-1)(y/3)#

#x-1=log^(-1)(y/3)#

#x=log^(-1)(y/3)+1#

Now swap the #x# and #y# giving:

#y=log^(-1)(x/3)+1#

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Answer 2

Lincoln Anderson

To find the inverse of the function (f(x) = 3\log(x - 1)), we switch the roles of (x) and (y) and solve for (y).

Start with the original function: (f(x) = 3\log(x - 1)).
Replace (f(x)) with (y): (y = 3\log(x - 1)).
Swap (x) and (y): (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]

So, the inverse function is (f^{-1}(x) = 10^{x/3} + 1).

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Answer from HIX Tutor

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.