Question

consider the function f(x)=2e^x/3e^x+1 from R to R. the inverse of f would be?
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Answer 1

Step-by-step explanation:

$Let \: \: y = f ^{ - 1} (x)$

$\implies f(y )= x$

$\implies \frac{2 {e}^{y} }{3 {e}^{y} + 1} = x$

$\implies 2 {e}^{y} = 3 x{e}^{y} +x$

$\implies 2 {e}^{y} - 3 x{e}^{y} = x$

$\implies (2 - 3 x){e}^{y} = x$

$\implies {e}^{y} = \frac{x}{(2 - 3 x)}$

$\implies y = \ln \bigg(\frac{x}{2 - 3 x} \bigg)$

Answer 2

Answer:

i don't know 2-2-2=

Step-by-step explanation: