To find the inverse function f−1(x)f^{-1}(x)f−1(x) for f(x)=1x+15f(x) = \frac{1}{x} + 15f(x)=x1​+15

To find the inverse of the function \( f(x) = \frac{1}{x} + 15 \), follow these steps:

### Step 1: Write the function as \( y = f(x) \)
\[
y = \frac{1}{x} + 15
\]

### Step 2: Solve for \( x \) in terms of \( y \)
First, subtract 15 from both sides to isolate the term involving \( x \):
\[
y - 15 = \frac{1}{x}
\]
Now, take the reciprocal of both sides to solve for \( x \):
\[
x = \frac{1}{y - 15}
\]

### Step 3: Replace \( y \) with \( x \) to find \( f^{-1}(x) \)
Thus, the inverse function is:
\[
f^{-1}(x) = \frac{1}{x - 15}
\]

So, the inverse function is:
\[
f^{-1}(x) = \frac{1}{x - 15}
\]

Would you like more details or clarifications?

Here are 5 related questions to explore:
1. How do we verify that two functions are inverses?
2. What happens to the domain and range when finding inverse functions?
3. How can inverse functions be applied to real-world problems?
4. What are the limitations when finding the inverse of a function?
5. How does the graph of a function compare to its inverse?

**Tip:** When checking if two functions are inverses, remember that \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).

To find the inverse function f−1(x) for f(x) = 1/x + 15

Learn how to find the inverse of the function f(x) = 1/x + 15. This problem explores key algebraic concepts, such as inverse functions and rational functions, with a step-by-step guide. Suitable for high school students in Grades 10-12.

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