What is the inverse of f(x)=-2log_{10}(2)(x-1)+2 ?

The inverse of f(x)=-2log_{10}(2)(x-1)+2 is -(x-2)/(2log_{10)(2)}+1

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inverse of f(x)=-2log_{10}(2)(x-1)+2

inverse

f (x) = - 2 lo g_{10} (2) (x - 1) + 2

- \frac{x - 2}{2 lo g _{10} ( 2 )} + 1

Solution steps

y = - 2 lo g_{10} (2) (x - 1) + 2

Replace

x

with

y

x = - 2 lo g_{10} (2) (y - 1) + 2

Solve for

y, x = - 2 lo g_{10} (2) (y - 1) + 2

- \frac{x - 2}{2 lo g _{10} ( 2 )} + 1

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

f (x) = - 5 x - 8

f (x) = 4 x (6 - x)

f (x) = \frac{2 x + 4}{3}

f (x) = 9 (x + 3)^{\frac{1}{3}}

What is the inverse of f(x)=-2log_{10}(2)(x-1)+2 ?
The inverse of f(x)=-2log_{10}(2)(x-1)+2 is -(x-2)/(2log_{10)(2)}+1