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

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

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

inverse

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

2^{\frac{x - 2}{3}} + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

2^{\frac{x - 2}{3}} + 1

f (x) = (x - 1) g (x) = x - 1

\frac{d}{d} \frac{5}{x}

f (x) = 6 + 2 x - 6

h (x) = (x)^{- 1} = x + 5

f (\frac{π}{6})

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