How do you find the inverse of $f(x)=2log(x+1)$ ?

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Answer 1 · 2015-12-12T17:25:19

I think this is how you write it! $color(white)(...)f^(-1)(x) = 10^(x/2)-1$

Consider log to base 10 of x =y

$log_10(x)=y$

From this we have: $10^y=x$

Now look at your question:

Write as: $y=2log_10(x+1)$

$y/2=log_10(x+1)$

so $10^(y/2)=x+1$

$x=10^(y/2)-1$

Now swap the y's and x's around

$y=10^(x/2)-1$

$f^(-1)(x) = 10^(x/2)-1$

How do you find the inverse of f(x)=2log(x+1)f(x)=2log(x+1)?