What is the inverse of f(x)=log_{e}((x+4)/x) ?

The inverse of f(x)=log_{e}((x+4)/x) is 4/(e^x-1)

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inverse of f(x)=log_{e}((x+4)/x)

inverse

f (x) = lo g_{e} (\frac{x + 4}{x})

\frac{4}{e ^{x} - 1}

Solution steps

y = lo g_{e} (\frac{x + 4}{x})

Replace

x

with

y

x = lo g_{e} (\frac{y + 4}{y})

Solve for

y, x = lo g_{e} (\frac{y + 4}{y})

\frac{4}{e ^{x} - 1}

f (x) = 2 x + 1

f (x) = 12 x^{2} - 3 x^{4}

(- 10, 6), (2, - 4)

\frac{1}{x - 3} + 4

2 x^{2} - 3

What is the inverse of f(x)=log_{e}((x+4)/x) ?
The inverse of f(x)=log_{e}((x+4)/x) is 4/(e^x-1)