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📈 Optional Mathematics - Class 10
Lesson 1 · Inverse Function

Inverse Function Presentation

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Optional Mathematics · Class 10 · Lesson 1

Inverse Function

Reverse the arrows · Swap x and y · Find f⁻¹(x)

By the end of this lesson you can

🔄

Explain what an inverse function is

✅

Say when an inverse function exists

🔗

Find f⁻¹ from ordered pairs

✏️

Find f⁻¹(x) from a formula

🧩

Use inverses with composite functions

Two functions, arrows reversed

❌f = {(1,0), (3,1), (5,0), (7,4)}
Reversed: {(0,1), (1,3), (0,5), (4,7)}
0 goes to two places: 1 and 5
-2 goes nowhere
Not a function
VS
✅g = {(1,3), (2,4), (3,5), (4,6)}
Reversed: {(3,1), (4,2), (5,3), (6,4)}
Every element has one partner
Nothing is left out
A function: this is g⁻¹

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Presenter notes: Today we ask what happens when we turn a function round and run it backwards. Sometimes we get a new function, and sometimes we do not.