Checking an Inverse
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 30 of 58.
A function and its inverse undo each other, so composing them gives back the input: f(f^-1(x)) = x. That is a test for any claimed inverse: compose the two and see whether x comes back.
Take p(x) = 4x - 3 and the claim q(x) = (x + 3)/4. Then p(q(x)) = 4 × (x + 3)/4 - 3. The 4s cancel, leaving x + 3 - 3, which is x. The claim passes.
A wrong guess fails in plain sight. Try r(x) = x/4 + 3: p(r(x)) = x + 12 - 3, which is x + 9, not x. The guess undid the steps in the wrong order: undoing times 4, then minus 3 means adding 3 first and dividing by 4 last.
Challenge
Is g the inverse of f? For f(x) = (x - 1)/2 and g(x) = 2x + 1, work out f(g(x)): use the inner rule, then the outer one, then type each simpler line. If x comes back, g undoes f.
Try it yourself
Simplify the expression
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 Flip6Inverse Functions
Undoing a FunctionSwap and SolveFractions in InversesChecking an InverseA Value of the InverseRecap: Inverses