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

The inverse of f(x)= 1/2 log_{2}(x-3)+2 is 2^{2x-4}+3

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

inverse

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

2^{2 x - 4} + 3

Solution steps

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

Replace

x

with

y

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

Solve for

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

2^{2 x - 4} + 3

(x + 2)^{2}

\frac{x - 4}{x + 2}

f (x) = \frac{- 2}{x - 7}

- 6 x + 2 y = - 8

y = - \frac{10}{x}

What is the inverse of f(x)= 1/2 log_{2}(x-3)+2 ?
The inverse of f(x)= 1/2 log_{2}(x-3)+2 is 2^{2x-4}+3