Find the inverse function of $$ f(x)=\sqrt{7 x+8} $$ $$ f^{-1}(x)=\square $$

Question

UpStudy AI · Accepted Answer

1. Start with the function:
   $$
   f(x)=\sqrt{7x+8}
   $$

2. Write the equation using $$ y $$:
   $$
   y=\sqrt{7x+8}
   $$

3. Swap $$ x $$ and $$ y $$ to find the inverse:
   $$
   x=\sqrt{7y+8}
   $$

4. Square both sides to eliminate the square root:
   $$
   x^2 = 7y+8
   $$

5. Solve for $$ y $$:
   $$
   7y = x^2 - 8
   $$
   $$
   y=\frac{x^2-8}{7}
   $$

6. Thus, the inverse function is:
   $$
   f^{-1}(x)=\frac{x^2-8}{7}
   $$
The inverse function is $$ f^{-1}(x) = \frac{x^2 - 8}{7} $$.

Find the inverse function of \( f(x)=\sqrt{7 x+8} \) \( f^{-1}(x)=\square \)