Grade X
ALGEBRA · फलन
Function फलन
Algebra — Grade X OPT Mathematics
📚 # Topics
📝 #+ Subtopics
🎯 K · U · A · HA
🔢 Nepal CDC
Function — Chapters
Click any topic to expand subtopics
Model Exercises
Exercise — Model 1 (Knowledge)
▼ Show
Exercise — Model 2 (Understanding)
▼ Show
Exercise — Model 3 (Application)
▼ Show
Exercise — Model 4 (Higher Ability)
▼ Show
Key Formulas
Essential formulas for Function chapter
Function Definitions
Function Notation
$$f: A \rightarrow B$$
A function maps each element of domain $A$ to exactly one element of codomain $B$.
Identity Function
$$I(x) = x$$
Every element maps to itself. $f(x) = ax+b$ is identity when $a=1, b=0$.
Composite Function
$$(g \circ f)(x) = g(f(x))$$
Apply $f$ first, then apply $g$ to the result. Order matters!
Inverse Function
$$f^{-1}(y) = x \iff f(x) = y$$
Swap $x$ and $y$, then solve for $y$ to find the inverse.
Composite & Inverse
$$(f \circ f^{-1})(x) = x$$
A function composed with its inverse gives the identity function.
Linear Function
$$f(x) = ax + b$$
Inverse: $f^{-1}(x) = \dfrac{x-b}{a}$, where $a \neq 0$.
Domain & Range
$$\text{Dom}(f^{-1}) = \text{Ran}(f)$$
The domain of the inverse equals the range of the original function.
Ordered Pair Inverse
$$(a, b) \in f \Rightarrow (b, a) \in f^{-1}$$
To find inverse from ordered pairs, simply swap each $(x,y)$ pair.
Key Concepts
Click a concept chip to learn more
🔢 What is a Function?
🆔 Identity Function
🧩 Composite Function
🔄 Inverse Function
📍 Domain & Range
📋 Ordered Pairs
📊 Types of Functions
⚙️ Into vs Onto
Old Questions
Previous SEE board exam questions
Click Show/Hide to reveal solutions.
Group A · 1 Mark
Knowledge Level Questions
▼
Group B · 2 Marks
Understanding Level Questions
▼
Group C · 3 Marks
Application Level Questions
▼
Group D · 4–5 Marks
Higher Ability Questions
▼
Learning Videos
Watch and learn — click to play
Click any video card to play directly.
▶
Lesson 1 · Function
Introduction to Functions
⏱ ~15 min
Learning Games
Play these interactive games to practise
No comments:
Post a Comment