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) = 2 \cdot 3^{x} + 9^{x} + 3

f (x) = 7 - 14 x

f (x) = - 1 - x^{3}

g (x) = 4 (x - 1)^{2}

f (x) = 10 x + 3

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