Fractions in Inverses
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 29 of 58.
When the rule divides, the inverse multiplies. Take f(x) = (x + 6)/2. Write y = (x + 6)/2 and swap: x = (y + 6)/2.
Clear the fraction first by multiplying both sides by 2: 2x = y + 6. Then subtract 6: y = 2x - 6. So f^-1(x) = 2x - 6. Check: f(4) is 5, and the inverse sends 5 to 10 minus 6, which is 4.
Notice the order. f adds 6, then halves. The inverse doubles, then takes 6 away: each step undone, in reverse order, like taking off shoes before socks.
Challenge
Find the inverse of f(x) = (x - 4)/3. The board holds the swapped equation: solve it for y.
Try it yourself
Solve for y
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