Reading inverse values from a graph

TL;DR

The video discusses finding the value of f inverse of two and sketching the graph of f inverse of x.

Transcript

• [Instructor] We're told the following graph shows y is equal to f of x, all right. And then the first question they say is, "What appears to be the value of f inverse of two?" Pause the video and see if you can have a go at that. All right, now let's work through this together. So it's important to realize they're not asking us what f of two is. ... Read More

Key Insights

• 🔢 The value of f inverse of a given number is found by identifying the corresponding input value on the graph of f.
• 👈 Swapping the x and y values of points on the original graph helps create corresponding points on the inverse graph.
• 🏙️ The graph of the inverse function is a reflection of the original function about the line y=x.

Questions & Answers

Q: What is the difference between f of x and f inverse of x?

f of x represents the output value obtained by inputting x into the function f, while f inverse of x represents the input value needed to obtain x as the output.

Q: How do you find the value of f inverse of a given number?

To find f inverse of a given number, you need to identify the corresponding input value on the graph of f by swapping the x and y values of the point.

Q: How does swapping points on the graph help in sketching the graph of f inverse of x?

Swapping the points from the original graph onto the inverse graph helps identify the corresponding points. Connecting these points will allow for the sketching of the inverse function's graph.

Q: What relationship exists between the graph of f and the graph of f inverse?

The graph of f inverse is a reflection of the graph of f about the line y=x. This means that the x and y values of each point are swapped to obtain corresponding points on the inverse graph.

Summary & Key Takeaways

• The video explains the process of finding the value of f inverse of two by swapping the x and y values on the graph.

• To sketch the graph of f inverse of x, points from the original graph f are swapped to create corresponding points on the inverse graph.

• The graph of the inverse function is a reflection of the original function f about the line y=x.