What is the inverse of f(x)= 1/3 ln((x+1)/2) ?

The inverse of f(x)= 1/3 ln((x+1)/2) is e^{3x}*2-1

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inverse of f(x)= 1/3 ln((x+1)/2)

inverse

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

e^{3 x} \cdot 2 - 1

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{1}{3} ln (\frac{y + 1}{2})

e^{3 x} \cdot 2 - 1

h (x) = \frac{x}{2 x + 1}

\frac{2 x - 7}{x + 4}

x^{2} - 10 x + 21

f (x) = \frac{( x + 1 )}{( x - 4 )}

y = \frac{1}{3} x^{3}

What is the inverse of f(x)= 1/3 ln((x+1)/2) ?
The inverse of f(x)= 1/3 ln((x+1)/2) is e^{3x}*2-1