Determine the inverse of $$ y=x^{7}+3 $$ A $$ y=\sqrt[7]{x+3} $$ B $$ y=\sqrt[7]{x}-3 $$ C $$ y=\sqrt[7]{x-3} $$ D $$ y=\frac{x+3}{7} $$

Question

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To find the inverse of the function $$ y = x^7 + 3 $$, follow these steps:

1. **Start with the original equation:**
   $$
   y = x^7 + 3
   $$

2. **Solve for $$ x $$ in terms of $$ y $$:**
   $$
   y - 3 = x^7
   $$
   $$
   x = \sqrt[7]{y - 3}
   $$

3. **Express the inverse function:**
   $$
   f^{-1}(y) = \sqrt[7]{y - 3}
   $$

4. **Rewrite in terms of $$ x $$:**
   $$
   f^{-1}(x) = \sqrt[7]{x - 3}
   $$

Among the given options, this corresponds to:

**C) $$ y = \sqrt[7]{x - 3} $$**

**Answer:** Option C) $$ y=\sqrt[7]{x-3} $$
The inverse of $$ y = x^7 + 3 $$ is $$ y = \sqrt[7]{x - 3} $$.

Determine the inverse of
A
B
C
D