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How to find the inverse of 3log3(x+3)+1. Its with a base of 3

User Defuera
by
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1 Answer

6 votes

Let
f^(-1)(x) be the inverse of


f(x) = 3 \log_3 (x + 3) + 1

Then by definition of inverse function,


f\left( f^(-1)(x) \right) = 3 \log_3 \left(f^(-1)(x) + 3\right) + 1 = x

Solve for the inverse :


3 \log_3 \left(f^(-1)(x) + 3\right) + 1 = x


3 \log_3 \left(f^(-1)(x) + 3\right) = x - 1


\log_3 \left(f^(-1)(x) + 3\right) = \frac{x - 1}3


3^{\log_3 \left(f^(-1)(x) + 3\right)} = 3^{\frac{x-1}3}


f^(-1)(x) + 3 = 3^{\frac{x-1}3}


f^(-1)(x) = 3^{\frac{x-1}3} - 3

User Yogie
by
7.1k points
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