What is the inverse of f(x)=3^{x+2}-6 ?

The inverse of f(x)=3^{x+2}-6 is (ln(x+6))/(ln(3))-2

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inverse of f(x)=3^{x+2}-6

inverse

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

\frac{ln ( x + 6 )}{ln ( 3 )} - 2

Solution steps

y = 3^{x + 2} - 6

Replace

x

with

y

x = 3^{y + 2} - 6

Solve for

y, x = 3^{y + 2} - 6

\frac{ln ( x + 6 )}{ln ( 3 )} - 2

2 + 4 + 7 x

f (x) = - 2 x^{2} - 12 x - 9

f (x) = \frac{13 x}{x - 4}

f (x) = ln (1 - 2 x)

2^{x} - 4

What is the inverse of f(x)=3^{x+2}-6 ?
The inverse of f(x)=3^{x+2}-6 is (ln(x+6))/(ln(3))-2