What is the inverse of f(x)=(5e^x-8)/(e^x+10) ?

The inverse of f(x)=(5e^x-8)/(e^x+10) is ln((-8-10x)/(x-5))

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inverse of f(x)=(5e^x-8)/(e^x+10)

inverse

f (x) = \frac{5 e ^{x} - 8}{e ^{x} + 10}

ln (\frac{- 8 - 10 x}{x - 5})

Solution steps

y = \frac{5 e ^{x} - 8}{e ^{x} + 10}

Replace

x

with

y

x = \frac{5 e ^{y} - 8}{e ^{y} + 10}

Solve for

y, x = \frac{5 e ^{y} - 8}{e ^{y} + 10}

ln (\frac{- 8 - 10 x}{x - 5})

f (x) = - 2 (x + 3)^{2} - 6

f (x) = 5 (x - 1)

(4, 2), (4, 0)

f (x) = \frac{( 2 x ^{3} + 3 x ^{2} )}{x ^{3} - 4 x}

f (x) = x^{2} + 2 x + 3

What is the inverse of f(x)=(5e^x-8)/(e^x+10) ?
The inverse of f(x)=(5e^x-8)/(e^x+10) is ln((-8-10x)/(x-5))