Final: Inside and Out
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 54 of 58.
This problem uses two functions, f(x) = 2x + 1 and g(x) = x^2. Compose them both ways, g inside f and f inside g, and subtract the second composition from the first. Write the result as one expression, multiplied out and collected.
Challenge
For f(x) = 2x + 1 and g(x) = x^2, simplify f(g(x)) - g(f(x)) into one expanded expression.
Try it yourself
f(g(x)) - g(f(x))
Multiply everything out
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Functions & Transformations
4Combining Functions
Adding FunctionsSubtracting FunctionsMultiplying FunctionsAt a Single NumberRecap: Combining10Functions in Stories
Writing the RuleUsing the RuleWorking BackwardUndoing a ConversionRecap: Stories2Expressions as Inputs
A Letter as InputA Sum as InputShifting the InputSolving f(x) = kRecap: Inputs as Expressions5Composition
One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip11Final Challenges
Final: Inside and OutFinal: The InverseFinal: Move the VFinal: Where f LivesFinal: The Rental