Suppose a function can be described by 𝑦=𝑓(𝑥). The graphs of the function and the inverse function intersect when𝑦=

To determine the value of $y$ at which the graphs of a function $y = f(x)$ and its inverse $y = f^{-1}(x)$ intersect, we can follow these steps:

1. Break Down the Problem

The intersection of the original function and its inverse occurs when both functions yield the same output for a given input. Mathematically, this means:

$f(x) = f^{-1}(x)$

2. Relevant Concepts

For a function and its inverse to intersect, the point of intersection must satisfy both equations simultaneously. This leads to:

$y = f(x) \quad \text{and} \quad x = f^{-1}(y)$

3. Analysis and Detail

From the above equations, if we take $x = y$, it means we are looking for points on the line $y = x$. Therefore, the intersection point will occur when:

$f(x) = x$

4. Verify and Summarize

To find the exact value of $y$ where the graphs intersect, we would need the specific function $f(x)$. In many cases including linear functions, this implies finding the fixed points of the function.

Final Answer

Thus, the graphs of the function $y = f(x)$ and its inverse intersect when $y = x$, meaning they cross along the line $y = x$, at the points where $f(x) = x$.