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

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

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

inverse

f (x) = 2^{x - 2} + 1

\frac{ln ( x - 1 )}{ln ( 2 )} + 2

Solution steps

y = 2^{x - 2} + 1

Replace

x

with

y

x = 2^{y - 2} + 1

Solve for

y, x = 2^{y - 2} + 1

\frac{ln ( x - 1 )}{ln ( 2 )} + 2

f (x) = 4 x - 3

f (x) = 1 - 21 x^{2}

f (x) = \frac{1 + 1}{( 1 + 0.15 \cdot 10 )}

f (x) = 2 (3 x + 1) + 4

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

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