For the following function, find $$ f^{-1} $$ $$ f(x)=3^{x+2} $$

Question

UpStudy AI · Accepted Answer

1. Let $$ y=f(x)=3^{x+2} $$.

2. To find the inverse function $$ f^{-1}(x) $$, swap $$ x $$ and $$ y $$:
   $$
   x = 3^{y+2}
   $$

3. Take the logarithm base 3 on both sides to solve for $$ y $$:
   $$
   \log_3(x) = y+2
   $$

4. Isolate $$ y $$ by subtracting 2:
   $$
   y = \log_3(x) - 2
   $$

5. Therefore, the inverse function is:
   $$
   f^{-1}(x)=\log_3(x)-2
   $$
The inverse function is $$ f^{-1}(x) = \log_3(x) - 2 $$.

For the following function, find