U1 Composite and inverse functions(KA/PRE/U1)

Unit 1: Composite and Inverse Functions

Composing Functions

When composing functions, the output of one function becomes the input of another. Example: f(g(x)).

Modeling with Composite Functions

Composite functions are used to model real-world problems with multiple steps. For example, converting units and then calculating costs.

Example: Celsius โ†’ Fahrenheit โ†’ Energy cost

Invertible Functions

A function is invertible if its graph passes the horizontal line test โ€” each output is mapped from exactly one input.

Inverse Functions in Graphs and Tables

Inverse functions reflect across the line y = x. On a graph, f(x) and its inverse are mirror images.

Verifying Inverse Functions by Composition

To verify that two functions are inverses, check if f(g(x)) = x and g(f(x)) = x.

Quiz: Test Your Understanding

Which of the following is true about inverse functions?

  1. They always pass through the origin.
  2. They reflect across y = x.
  3. They are always linear.

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