1/x find the inverse of the following function 

To find the inverse of a function, we reverse the roles of \( x \) and \( y \), and then solve for \( y \).

Given function:

\[
f(x) = \frac{1}{x}
\]

### Steps to find the inverse:

1. Start by writing the function as \( y = \frac{1}{x} \).
2. Switch \( x \) and \( y \) to reflect the inverse: 
   \[
   x = \frac{1}{y}
   \]
3. Solve for \( y \):
   \[
   y = \frac{1}{x}
   \]

Thus, the inverse of the function \( f(x) = \frac{1}{x} \) is:

\[
f^{-1}(x) = \frac{1}{x}
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the inverse of the function \( f(x) = 2x + 3 \)?
2. How can you verify if a function and its inverse are correct?
3. Is the function \( f(x) = \frac{1}{x} \) one-to-one and onto?
4. What is the domain and range of \( f(x) = \frac{1}{x} \) and its inverse?
5. How would you find the inverse of \( f(x) = \frac{1}{x + 2} \)?

**Tip:** A function must be one-to-one (bijective) for it to have an inverse. This means it passes both the horizontal line test and is onto.

1/x find the inverse of the following function

Learn how to find the inverse of the function f(x) = 1/x through step-by-step instructions. This problem covers the algebraic process of switching variables and solving for the inverse. Ideal for high school students in Grades 10-12.

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