What is the inverse of f(x)=(2e^x-10)/(22e^x+14) ?

The inverse of f(x)=(2e^x-10)/(22e^x+14) is ln(-(7x+5)/(11x-1))

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inverse of f(x)=(2e^x-10)/(22e^x+14)

inverse

f (x) = \frac{2 e ^{x} - 10}{22 e ^{x} + 14}

ln (- \frac{7 x + 5}{11 x - 1})

Solution steps

y = \frac{2 e ^{x} - 10}{22 e ^{x} + 14}

Replace

x

with

y

x = \frac{2 e ^{y} - 10}{22 e ^{y} + 14}

Solve for

y, x = \frac{2 e ^{y} - 10}{22 e ^{y} + 14}

ln (- \frac{7 x + 5}{11 x - 1})

y = 0.0292 \cdot x^{2} + 1.067 \cdot x + 1

y = x^{2}

f (x) = \frac{x}{7} - 3

f (x) = 1 - x

f (x) = 0.73

What is the inverse of f(x)=(2e^x-10)/(22e^x+14) ?
The inverse of f(x)=(2e^x-10)/(22e^x+14) is ln(-(7x+5)/(11x-1))