Solving f(x) = k
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 9 of 58.
Evaluating runs a function forwards: input in, output out. Solving runs it backwards: you know the output and want the input. f(x) = 11 asks which inputs make the output 11.
Use the rule to turn it into an ordinary equation. For f(x) = 2x + 3, the question f(x) = 11 becomes 2x + 3 = 11, so x = 4. Check it forwards: f(4) is 8 + 3, which is 11.
A function can reach the same output from more than one input. For g(x) = x^2 + 2, the question g(x) = 27 becomes x^2 = 25, which has two solutions, 5 and -5. Both are answers, so a full solution names both.
Challenge
For f(x) = x^2 - 1, solve f(x) = 8. Give every input that works.
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 Flip