How do you find the inverse of $f(x)= (100)/(1+2^-x)$ ?

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Answer 1 · 2015-12-17T16:11:47

$y=-log_2((100-x)/x)$

Rewrite as

$y=100/(1+2^-x)$

Flip the $x$ and $y$ and solve for $y$ .

$x=100/(1+2^-y)$

$x(1+2^-y)=100$

$1+2^-y=100/x$

$2^-y=100/x-1$

$2^-y=(100-x)/x$

$-y=log_2((100-x)/x)$

$y=-log_2((100-x)/x)$

The graphs should be reflections of themselves over the line $y=x$ .

How do you find the inverse of f(x)= (100)/(1+2^-x)f(x)= (100)/(1+2^-x)?