Question 22 Consider the function $$ f(x)=\sqrt{x+3} $$ Find the formula for the inverse function. $$ f^{-1}(x)=\frac{1}{\sqrt{x-3}} $$ $$ f^{-1}(x)=x^{2}-3 $$ $$ f^{-1}(x)=x^{2}+3 $$ $$ f^{-1}(x)=\frac{1}{\sqrt{x+3}} $$

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To find the inverse of the function $$ f(x) = \sqrt{x + 3} $$, follow these steps:

1. **Start with the function definition:**
   $$
   y = \sqrt{x + 3}
   $$

2. **Swap $$ x $$ and $$ y $$ to begin finding the inverse:**
   $$
   x = \sqrt{y + 3}
   $$

3. **Solve for $$ y $$:**
   - Square both sides to eliminate the square root:
     $$
     x^2 = y + 3
     $$
   - Isolate $$ y $$:
     $$
     y = x^2 - 3
     $$

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

**Answer:**  
$$ f^{-1}(x)=x^{2}-3 $$
$$ f^{-1}(x) = x^{2} - 3 $$

Question 22
Consider the function
Find the formula for the inverse function.

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Question 22 Consider the function Find the formula for the inverse function.