What is the inverse of f(x)= 8/(e^{x-3)+6} ?

The inverse of f(x)= 8/(e^{x-3)+6} is ln(8/x-6)+3

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inverse of f(x)= 8/(e^{x-3)+6}

inverse

f (x) = \frac{8}{e ^{x - 3} + 6}

ln (\frac{8}{x} - 6) + 3

Solution steps

y = \frac{8}{e ^{x - 3} + 6}

Replace

x

with

y

x = \frac{8}{e ^{y - 3} + 6}

Solve for

y, x = \frac{8}{e ^{y - 3} + 6}

ln (\frac{8}{x} - 6) + 3

f (x) = 25 x - 18

f (x) = \frac{2 x - 5}{x - 7}

f (x) = \frac{( 3 x - 1 )}{x + 2}

f (x) = 100 - (x + 5)^{2}

y = 3 - 4 x

What is the inverse of f(x)= 8/(e^{x-3)+6} ?
The inverse of f(x)= 8/(e^{x-3)+6} is ln(8/x-6)+3