What is the inverse of f(x)=2^{(x+1)/(x-1)} ?

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

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inverse of f(x)=2^{(x+1)/(x-1)}

inverse

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

\frac{ln ( 2 x )}{ln ( x ) - ln ( 2 )}

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = 2^{\frac{y + 1}{y - 1}}

\frac{ln ( 2 x )}{ln ( x ) - ln ( 2 )}

(1 + 3 x)^{5}

f (x) = 8 x + 10

f (x) = 8 x + 16

lo g_{10} (2) (k x - 10)

f (x) = 4 x^{\frac{1}{5}} + 2

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