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

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

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

inverse

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

2^{x + 2} + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

2^{x + 2} + 1

f (x) = 4^{x} + 2

f (x) = 3 x^{\frac{2}{3}} + x^{\frac{5}{3}}

f (x) = 2 x (4 - x)^{3}

x = y

f (x) = x^{2} - 2 x + 5

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