What is the inverse of f(x)=log_{3}(1-2x+x^2) ?

The inverse of f(x)=log_{3}(1-2x+x^2) is 1+sqrt(3^x),1-sqrt(3^x)

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inverse of f(x)=log_{3}(1-2x+x^2)

inverse

f (x) = lo g_{3} (1 - 2 x + x^{2})

1 + 3^{x}, 1 - 3^{x}

Solution steps

y = lo g_{3} (1 - 2 x + x^{2})

Replace

x

with

y

x = lo g_{3} (1 - 2 y + y^{2})

Solve for

y, x = lo g_{3} (1 - 2 y + y^{2})

1 + 3^{x}, 1 - 3^{x}

f (x) = \frac{e ^{x} - 6}{3 - e ^{x}}

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

\frac{2 x + 7}{2}

f (x) = \frac{x}{8 x - 5}

f (x) = (5 x + 10)^{\frac{1}{2}} + 14

What is the inverse of f(x)=log_{3}(1-2x+x^2) ?
The inverse of f(x)=log_{3}(1-2x+x^2) is 1+sqrt(3^x),1-sqrt(3^x)