What is the inverse of f(x)=ln(x+4)-ln(x-1) ?

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

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inverse of f(x)=ln(x+4)-ln(x-1)

inverse

f (x) = ln (x + 4) - ln (x - 1)

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

Solution steps

y = ln (x + 4) - ln (x - 1)

Replace

x

with

y

x = ln (y + 4) - ln (y - 1)

Solve for

y, x = ln (y + 4) - ln (y - 1)

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

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

2 x^{2} - 4

y = \frac{4 x + 4}{x - 4}

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

f (x) = 7 x + 9 x + 2

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