44. What is the inverse of $$ f(x)=2^{x}-3 $$ ? A. $$ f^{-1}(x)=\log _{3}(x+2) $$ B. $$ f^{-1}(x)=\log _{2}(x+3) $$ C. $$ f^{-1}(x)=\log _{3}(x-2) $$ D. $$ f^{-1}(x)=\log _{2}(x-3) $$

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To find the inverse of the function $$ f(x) = 2^{x} - 3 $$, follow these steps:

1. **Start with the original equation:**
   $$
   y = 2^{x} - 3
   $$

2. **Solve for $$ 2^{x} $$:**
   $$
   y + 3 = 2^{x}
   $$

3. **Take the logarithm with base 2 on both sides to solve for $$ x $$:**
   $$
   x = \log_{2}(y + 3)
   $$

4. **Express the inverse function:**
   $$
   f^{-1}(x) = \log_{2}(x + 3)
   $$

So, the inverse function is $$ f^{-1}(x) = \log_{2}(x + 3) $$.

**Answer:**  
B. $$ f^{-1}(x)=\log _{2}(x+3) $$
The inverse function is $$ f^{-1}(x) = \log_{2}(x + 3) $$, so the correct choice is B.

What is the inverse of ?
A.
B.
C.
D.

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