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

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

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

inverse

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

\frac{ln ( x - 1 )}{ln ( 3 )} + 2

Solution steps

y = 3^{x - 2} + 1

Replace

x

with

y

x = 3^{y - 2} + 1

Solve for

y, x = 3^{y - 2} + 1

\frac{ln ( x - 1 )}{ln ( 3 )} + 2

f (x) = 3^{x - 2} + 4

f (x) = (2 x - 3)^{6} - 8

2^{x + 3} - 4

f (x) = \frac{7 x}{2} + 3

f (x) = 2^{3 x}

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