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Final: The Inverse

Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 52 of 55.

This problem asks for the inverse of $f\left(x\right) = \frac{3x+2}{4}$ , a rule that ends with a division. The board already holds the equation with x and y swapped. Solve it for y, and write the answer multiplied out.

Challenge

Find the inverse of $f\left(x\right) = \frac{3x+2}{4}$ . The board holds the swapped equation $x = \frac{3y+2}{4}$ : solve it for y and write the answer multiplied out.

Try it yourself

x = \frac{3y+2}{4}

Get $y$ alone, and multiply out the other side

Test yourself

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

All lessons in Functions & Transformations

1Rules That Draw

Meet f(x)Negative Inputs Shifting the Input Solving f(x) = k

4Combining Functions

Adding Functions Subtracting Functions Multiplying Functions At a Single Number Recap: Combining

7Shifting Graphs

Up and Down Left and Right The Sign Inside Both at Once Shifting a V Recap: Shifts

10Functions in Stories

Writing the Rule Using the Rule Working Backward Undoing a Conversion Recap: Stories

2Expressions as Inputs

A Sum as Input Solving a Shifted Rule Recap: Inputs as Expressions

5Composition

One Inside Another Order Matters A Function of Itself Composing Rules Breaking Apart Recap: Composition

8Stretching and Flipping

Taller and Flatter Flipping Over Flip, Then Shift Reading the Rule Recap: Stretch and Flip

11Final Challenges

Final: Inside and OutFinal: The InverseFinal: Move the V Final: Where f Lives Final: The Rental

3Domain and Range

What the Domain Is No Dividing by Zero No Roots of Negatives The Range Recap: Domain

6Inverse Functions

Undoing a Function Swap and Solve Fractions in Inverses Checking an Inverse A Value of the Inverse Recap: Inverses

9Rate of Change

Average Rate of Change A Line Keeps Its Rate A Curve Changes Rate Velocity as a Rate Recap: Rate of Change