Find the inverse function of f(x)=10+x3.
f-1(x)= 






To find the inverse of the function \( f(x) = 10 + x^3 \), follow these steps:

1. **Start by rewriting the function:**
   \[
   y = 10 + x^3
   \]
   where \( f(x) = y \).

2. **Swap \(x\) and \(y\) to find the inverse:**
   \[
   x = 10 + y^3
   \]

3. **Solve for \(y\):**
   \[
   x - 10 = y^3
   \]
   \[
   y = \sqrt[3]{x - 10}
   \]

So, the inverse function is:
\[
f^{-1}(x) = \sqrt[3]{x - 10}
\]

Would you like more details on how this process works? 

Here are some related questions:
1. How do you verify if two functions are inverses of each other?
2. What are the domain and range of the inverse function \( f^{-1}(x) \)?
3. How do the transformations of a function affect its inverse?
4. How do you graph a function and its inverse?
5. How does the cubic root function behave as compared to the cubic function?

**Tip:** When solving for an inverse function, always swap \( x \) and \( y \), and then isolate \( y \).

Find the inverse function of f(x)=10+x^3.

Learn how to find the inverse function of f(x) = 10 + x^3. This problem explains the step-by-step process to solve for the inverse function using algebraic manipulation and cubic root properties. Ideal for high school students in Grades 10-12.

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