What is the inverse of f(x)= 2/(log_{3)(x)} ?

The inverse of f(x)= 2/(log_{3)(x)} is 3^{2/x}

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inverse of f(x)= 2/(log_{3)(x)}

inverse

f (x) = \frac{2}{lo g _{3} ( x )}

3^{\frac{2}{x}}

Solution steps

y = \frac{2}{lo g _{3} ( x )}

Replace

x

with

y

x = \frac{2}{lo g _{3} ( y )}

Solve for

y, x = \frac{2}{lo g _{3} ( y )}

3^{\frac{2}{x}}

\frac{x ^{2} + 1}{x}

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

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

f (x) = - 4 x - 8 + 10

f (x) = 100 \cdot x

What is the inverse of f(x)= 2/(log_{3)(x)} ?
The inverse of f(x)= 2/(log_{3)(x)} is 3^{2/x}