What is the inverse of f(x)=5-2^{x-1} ?

The inverse of f(x)=5-2^{x-1} is (ln(5-x))/(ln(2))+1

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inverse of f(x)=5-2^{x-1}

inverse

f (x) = 5 - 2^{x - 1}

\frac{ln ( 5 - x )}{ln ( 2 )} + 1

Solution steps

y = 5 - 2^{x - 1}

Replace

x

with

y

x = 5 - 2^{y - 1}

Solve for

y, x = 5 - 2^{y - 1}

\frac{ln ( 5 - x )}{ln ( 2 )} + 1

f (x) = \frac{( x + 14 )}{( x - 12 )}

f (x) = 2 x + 3

f (x) = \frac{5}{x ^{2} + 5 x - 6}

f (x) = 5^{- x}

\frac{4 x}{x - 2}

What is the inverse of f(x)=5-2^{x-1} ?
The inverse of f(x)=5-2^{x-1} is (ln(5-x))/(ln(2))+1