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

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

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

inverse

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

2^{x - 3} + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

2^{x - 3} + 1

\frac{( x + 5 )}{( x + 6 )}

5 x + 10

f (x) = x^{2} - 16 x, x \geq 8

f (x) = \frac{x - 7}{( x - 7 ) ( x - 5 )}

f (x) = 3 (x - 1)

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