What is the inverse of f(x)=(5^x)/(8+5^x) ?

The inverse of f(x)=(5^x)/(8+5^x) is (ln(-\frac{8x)/(x-1))}{ln(5)}

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inverse of f(x)=(5^x)/(8+5^x)

inverse

f (x) = \frac{5 ^{x}}{8 + 5 ^{x}}

\frac{ln ( - \frac{8 x}{x - 1} )}{ln ( 5 )}

Solution steps

y = \frac{5 ^{x}}{8 + 5 ^{x}}

Replace

x

with

y

x = \frac{5 ^{y}}{8 + 5 ^{y}}

Solve for

y, x = \frac{5 ^{y}}{8 + 5 ^{y}}

\frac{ln ( - \frac{8 x}{x - 1} )}{ln ( 5 )}

y - 10 = - 2 (x - 3)

- 36000 + 0.2 w

f (x) = cot^{2} (x)

(- 5.3) (2.7)

(- 2, 1), (3, - 1)

What is the inverse of f(x)=(5^x)/(8+5^x) ?
The inverse of f(x)=(5^x)/(8+5^x) is (ln(-\frac{8x)/(x-1))}{ln(5)}