A Value of the Inverse
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 31 of 58.
You do not need the whole inverse rule to find one value of it. g^-1(23) asks: which input does g send to 23? So write g(x) = 23 and solve for x.
Take g(x) = 3x + 2. Using the rule turns the question into 3x + 2 = 23, so 3x = 21 and x is 7. That means g^-1(23) = 7. Check forwards: g(7) is 21 + 2, which is 23.
This works because the inverse swaps inputs and outputs: g sends 7 to 23 exactly when its inverse sends 23 to 7. Solving one equation is quicker than finding the full inverse rule and then evaluating it.
Challenge
For f(x) = 4x - 5, find f^-1(15). The board holds f(x) = 15, which asks for the input that f sends to 15. Solve it.
Try it yourself
Solve for x
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