Florida B.E.S.T. MA.912.F.3.7
The Standard
Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students reverse a function by exchanging inputs and outputs, then express the result with an equation, graph, or table. They compose the functions in both orders to confirm each result is x.
What Mastery Looks Like
- Students can produce a correct inverse equation and match corresponding points in tables and graphs. They check both compositions and account for needed domain restrictions.
Common Misconceptions
- Students may confuse an inverse function with the reciprocal, writing 1/f(x). They may swap x and y without solving for y, ignore domain restrictions, or verify only one composition.
How to Assess It
- Give f(x) = 3x - 5. Ask students to find f⁻¹(x), then show that both compositions simplify to x.
Lesson moves
Ways to Teach It
Plot a function on graph paper, fold along y = x, and trace the reflected points to create its inverse.
Ask students to explain why f(x) = x² needs a restricted domain before its inverse can be a function.
Give groups cards showing equations, graphs, tables, and compositions, then have them match each function with its inverse.
Use Celsius and Fahrenheit conversion formulas, then have students reverse the conversion and verify both directions.
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Related Standards
- MA.912.F.3.4
Represent the composition of two functions algebraically or in a table. Determine the domain and range of the composite function.
- MA.912.C.2.6
Find derivatives of inverse functions.
- MA.912.F.3.9
Solve mathematical and real-world problems involving inverse functions.
- MA.912.F.3.6
Determine whether an inverse function exists by analyzing tables, graphs and equations.
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