In Function Inverses topic, 11th Grade students will learn how to reverse a function and how to combine functions. Students will learn what it means for a function to be one to one. Students will learn how compositions work and how order matters. Students will also learn how inverse and original functions connect on a graph.
Students learn to compute f of g of x and g of f of x and compare results. They learn how domain restrictions affect composition. They learn the horizontal line test for one to one functions. They practice finding inverses by swapping x and y and solving for y. They learn how to verify inverses using composition to get x. They learn graphs of inverses reflect across the line y equals x. They also learn inverse relationships for exponential and logarithmic functions.
1. If f x equals 2x plus 1, what is f inverse of x
A. x minus 1 over 2
B. 2x minus 1
C. x plus 1 over 2
D. 1 over 2x plus 1
2. Fill in the blank: f of f inverse of x equals ___ when defined
3. If g x equals x squared and f x equals x plus 3, what is g of f of x
A. x squared plus 3
B. x plus 3 squared
C. x squared plus 6x plus 9
D. x squared plus 9
4. Fill in the blank: A function must be ___ to have an inverse function
5. Thinking question: Why can restricting the domain of a function make an inverse possible
Inverses and composition help students model multi step processes. They support solving equations and understanding input output systems. Students learn to work carefully with order and domain. These ideas appear in coding, science formulas, and data transforms. The skills also prepare students for advanced function work in calculus. Clear inverse thinking builds strong algebra control.
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