Lesson Notes By Weeks and Term v4 - SHS 1
APPLICATIONS OF ALGEBRA
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APPLICATIONS OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 11
Grade code: 1.1.2.LI.6
Strand code: 1
Sub-strand code: 2
Content standard code: 1.1.2.CS.1
Indicator code: 1.1.2.LI.6
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATIONS OF ALGEBRA
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My dear learners, in our daily lives, we often perform actions and then need a way to "undo" them. For example, if you lock a door, the "undo" action is to unlock it. If you travel from Accra to Kumasi, the "undo" journey is from Kumasi back to Accra. In mathematics, functions transform numbers according to a rule. Inverse functions are the special "undo" rules that take the result and give you back the original number. This concept is powerful in many fields, from converting currencies when shopping online to cryptography (coding and decoding messages). Today, we will learn how to find these "undo" functions both by using algebra and by understanding their graphs.
A. What is an Inverse Function?
Think of a function as a machine. You put an input (x) in, and it gives you a unique output (y or f(x)). Function f: `Input (x)` → [Function Rule] → `Output (y)`
An inverse function, written as f⁻¹(x), is a machine that does the exact opposite. It takes the output (y) from the first machine and gives you back the original input (x). Inverse Function f⁻¹: `Output (y)` → [Inverse Rule] → `Input (x)`
So, if a function `f` takes an element `a` to `b`, (i.e., f(a) = b), then its inverse function `f⁻¹` must take `b` back to `a` (i.e., f⁻¹(b) = a).