Let `f(x)=x^(3)+3` be bijective, then find its inverse.

Answer

To find the inverse of the function \( f(x) = x^3 + 3 \), we will follow these steps:

### Step 1: Set the function equal to \( y \)
We start by letting \( y = f(x) \):
\[ y = x^3 + 3 \]

### Step 2: Solve for \( x \)
Next, we need to express \( x \) in terms of \( y \). We can rearrange the equation:
\[ y - 3 = x^3 \]
Now, we take the cube root of both sides to solve for \( x \):
\[ x = \sqrt[3]{y - 3} \]

### Step 3: Write the inverse function
To find the inverse function, we switch \( x \) and \( y \). This means we replace \( y \) with \( x \):
\[ f^{-1}(x) = \sqrt[3]{x - 3} \]

### Final Answer
Thus, the inverse function is:
\[ f^{-1}(x) = \sqrt[3]{x - 3} \]

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