Introduction to Inverse Functions and Graphing Techniques

The video tutorial covers the concept of inverse functions, demonstrating with functions FX and GX. It explains how to verify inverse functions through composition and illustrates graphing these functions, highlighting their symmetry about the line Y=X. The tutorial then delves into finding inverses of quadratic functions, discussing domain restrictions to ensure one-to-one mappings. The video emphasizes the relationship between the domain and range of functions and their inverses.

What is the result of FG(x) when F and G are inverse functions?

• 2x

• x

• x + 4

• 2x - 4

How can you graphically determine the inverse of a function?

• By rotating the graph 90 degrees

• By reflecting the graph over the line y = x

• By shifting the graph upwards

• By reflecting the graph over the x-axis

What is the inverse of the function F(x) = 2x - 4?

• x - 4 / 2

• x + 4 / 2

• 2x + 4

• x - 2

Why is it necessary to restrict the domain of a quadratic function when finding its inverse?

• To simplify the calculation

• To make the graph symmetrical

• To ensure the inverse is a one-to-one function

• To avoid negative values

What is the domain of the inverse function if the original quadratic function has a range of f(x) ≥ 5?

• x > 0

• x ≥ 0

• x ≥ 5

• x ≤ 5