What is the inverse of f(x)=9^x+2*3^x+3 ?

The inverse of f(x)=9^x+2*3^x+3 is (ln(-1+sqrt(x-2)))/(ln(3)),(ln(-sqrt(x-2)-1))/(ln(3))

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inverse of f(x)=9^x+2*3^x+3

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = 9^{y} + 2 \cdot 3^{y} + 3

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

What is the inverse of f(x)=9^x+2*3^x+3 ?
The inverse of f(x)=9^x+2*3^x+3 is (ln(-1+sqrt(x-2)))/(ln(3)),(ln(-sqrt(x-2)-1))/(ln(3))