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

4 x + 5 y = 16

x^{3} - \frac{15}{2} x^{2} - 18 x - 1

x^{3} - 18 \cdot x^{2} + 105 \cdot x + 9

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

f (x) = \frac{( 4 )}{( x ^{2} - 4 )}

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