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?
- They always pass through the origin.
- They reflect across y = x.
- They are always linear.
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