Find the Input

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 39 of 64.

The question also runs backwards: which input gives a wanted output? "Find x with f(x) = 11" for f(x) = 3x + 2 unfolds the name into its rule and solves:

3x + 2 = 11

3x = 9

x = 3

Evaluating goes input to output; solving goes output back to input. Same rule, opposite directions.

The unfold step, replacing f(x) by what it stands for, is the only new move; everything after it is the equation solving of the first section.

Challenge

The rule is f(x) = 3x + 2. Solve f(x) = 11 for x.

Try it yourself

f(x) = 11

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Graphs & Systems

1The Coordinate Plane

Two Numbers, One Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes Points The Points Line Up On the Line or Not?Between the Dots Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With SignsFind the InputThe Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods