What is the inverse of f(x)=1-2log_{5}(x) ?

The inverse of f(x)=1-2log_{5}(x) is 5^{-(x-1)/2}

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inverse of f(x)=1-2log_{5}(x)

inverse

f (x) = 1 - 2 lo g_{5} (x)

5^{- \frac{x - 1}{2}}

Solution steps

y = 1 - 2 lo g_{5} (x)

Replace

x

with

y

x = 1 - 2 lo g_{5} (y)

Solve for

y, x = 1 - 2 lo g_{5} (y)

5^{- \frac{x - 1}{2}}

f (x) = - x + 1

f (x) = x^{2} - x - 2

\frac{4 x - 9}{5 x + 3}

27 - x^{3}

f (x) = \frac{x - 3}{x ^{2} - 3 x + 9}

What is the inverse of f(x)=1-2log_{5}(x) ?
The inverse of f(x)=1-2log_{5}(x) is 5^{-(x-1)/2}