What is the inverse of f(x)= 1/(1+log_{10)(x)} ?

The inverse of f(x)= 1/(1+log_{10)(x)} is 10^{1/x-1}

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inverse of f(x)= 1/(1+log_{10)(x)}

inverse

f (x) = \frac{1}{1 + lo g _{10} ( x )}

1 0^{\frac{1}{x} - 1}

Solution steps

y = \frac{1}{1 + lo g _{10} ( x )}

Replace

x

with

y

x = \frac{1}{1 + lo g _{10} ( y )}

Solve for

y, x = \frac{1}{1 + lo g _{10} ( y )}

1 0^{\frac{1}{x} - 1}

What is the inverse of f(x)= 1/(1+log_{10)(x)} ?
The inverse of f(x)= 1/(1+log_{10)(x)} is 10^{1/x-1}