Mathematics With Sajid Hussain

Mathematics With Sajid Hussain A place where mathematics becomes easy and enjoyable. Helping students understand every concept clearly and confidently through Mathematics with Sajid Hussain.

📘 Chapter 3 – Sets and Functions | Part 28: Composition of FunctionsWhen two functions are combined, the output of one b...
14/08/2026

📘 Chapter 3 – Sets and Functions | Part 28: Composition of Functions

When two functions are combined, the output of one becomes the input of another.

🧠 Quick Quiz:
If f(x)=2x and g(x)=x+3, find (f∘g)(x).

A) 2x + 3
B) 2x + 6
C) x + 6

💬 Comment your answer!

🇵🇰 14 August Mubarak! 🇵🇰The Best English Grammar School, Mianwali (Ramzan Abad) کی جانب سے تمام اہلِ وطن کو یومِ آزادی م...
14/08/2026

🇵🇰 14 August Mubarak! 🇵🇰
The Best English Grammar School, Mianwali (Ramzan Abad)
کی جانب سے تمام اہلِ وطن کو یومِ آزادی مبارک! 💚
🎓 Admissions Open | PG to 8th
📚 Hussain Science Academy | Middle to F.Sc
تعلیم، تربیت اور روشن مستقبل کی ضمانت ✨
📞 0304-2827461
پاکستان زندہ باد 🇵🇰
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🗣️ Spoken English Course — Physical Classes in Mianwali City!👩‍🏫 Female Teaching Staff | 👧 Separate Classes for Girls🏫 T...
13/08/2026

🗣️ Spoken English Course — Physical Classes in Mianwali City!
👩‍🏫 Female Teaching Staff | 👧 Separate Classes for Girls

🏫 The Best English Grammar School Mianwali
📍 Near Al-Umer Masjid, Ramzan Abad, Mianwali
📢 Admissions Open — PG/Nursery to Class 8
📞 0304-2827461 | Sajid Hussain (School Principal)

📘 Class 9 Mathematics | Greek Letters Commonly Used in MathematicsIn this lesson, learn the Greek letters, their symbols...
13/08/2026

📘 Class 9 Mathematics | Greek Letters Commonly Used in Mathematics
In this lesson, learn the Greek letters, their symbols, and names commonly used in Mathematics, including α (Alpha), β (Beta), γ (Gamma), Δ (Delta), θ (Theta), λ (Lambda), μ (Mu), π (Pi), σ (Sigma), φ (Phi), ψ (Psi), and ω/Ω (Omega). ✨
These symbols are widely used in Algebra, Geometry, Trigonometry, Statistics, Probability, Calculus, Physics, Engineering, and Computer Science.
🧠 Quick Quiz: Which Greek letter represents the ratio of the circumference to the diameter of a circle?
A) α B) π C) σ
💬 Comment your answer below!
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📘 Chapter 3 – Sets and Functions | Part 27: Inverse FunctionAn Inverse Function reverses the mapping of a function.Iff(a...
13/08/2026

📘 Chapter 3 – Sets and Functions | Part 27: Inverse Function

An Inverse Function reverses the mapping of a function.

If
f(a) = b
then
f⁻¹(b) = a

📌 Remember: An inverse function exists when the function is Bijective (One-One and Onto).

Example

f = {(1,a), (2,b), (3,c)}

Therefore,

f⁻¹ = {(a,1), (b,2), (c,3)}

🧠 Quick Quiz:
If f = {(1,a),(2,b),(3,c)}, then what is f⁻¹?

A) {(a,1),(b,2),(c,3)}
B) {(1,a),(2,b),(3,c)}
C) {(a,2),(b,3),(c,1)}

💬 Comment your answer!

📘 Chapter 3 – Sets and Functions | Part 26: Bijective FunctionA Bijective Function is a function that is both One-One an...
12/08/2026

📘 Chapter 3 – Sets and Functions | Part 26: Bijective Function
A Bijective Function is a function that is both One-One and Onto.
📌 Remember:
Bijective = One-One + Onto
➡️ Different inputs have different outputs.
➡️ Every element of the codomain has a pre-image.
Example
f = {(1,a),(2,b),(3,c)}
Here, all outputs are different and every element of B is used, so f is Bijective.
🧠 Quick Quiz:
Which is a Bijective Function?
A) {(1,a),(2,b),(3,c)}
B) {(1,a),(2,a),(3,b)}
C) {(1,a),(2,b)}
💬 Comment your answer!

📘 Chapter 3 – Sets and Functions | Part 25: Into FunctionAn Into Function � is a function in which at least one element ...
11/08/2026

📘 Chapter 3 – Sets and Functions | Part 25: Into Function
An Into Function � is a function in which at least one element of the codomain has no pre-image in the domain.
📌 Remember:
Into → At least one element of B is left unused.
Onto → Every element of B is used.
Example
A = {1,2,3}, B = {a,b,c,d}
f = {(1,a),(2,b),(3,c)}
Here, d has no pre-image, so f is Into.
🧠 Quick Quiz:
Which is an Into Function?
A) {(1,a),(2,b),(3,c)}
B) {(1,a),(2,b),(3,c),(3,d)}
C) {(1,a),(2,b),(3,d)}
💬 Comment your answer!

📘 Chapter 3 – Sets and Functions | Part 24: Onto FunctionAn Onto Function � is a function in which every element of the ...
10/08/2026

📘 Chapter 3 – Sets and Functions | Part 24: Onto Function
An Onto Function � is a function in which every element of the codomain B has at least one pre-image in A.
📌 Remember:
Onto → Every element of B is used.
Example
A = {1,2,3}, B = {a,b}
f = {(1,a),(2,b),(3,a)}
Since both a and b have pre-images, f is Onto.
❌ If any element of B has no pre-image, the function is Not Onto.
🧠 Quick Quiz:
If A = {1,2,3} and B = {a,b}, which is Onto?
A) {(1,a),(2,b),(3,a)}
B) {(1,a),(2,a),(3,a)}
C) Both A and B
💬 Comment your answer!

📘 Chapter 3 – Sets and Functions | Part 23: One-One FunctionA One-One Function is a function in which different elements...
10/08/2026

📘 Chapter 3 – Sets and Functions | Part 23: One-One Function
A One-One Function is a function in which different elements of the domain have different images in the codomain.
📌 Remember:
Different Inputs → Different Outputs
Example
f = {(1,a), (2,b), (3,c)}
Since no two different inputs have the same output, f is a One-One Function.
❌ Not One-One:
f = {(1,a), (2,a), (3,b)}
Here, 1 and 2 have the same image a.
🧠 Quick Quiz:
Which is a One-One Function?
A) {(1,a), (2,b), (3,c)}
B) {(1,a), (2,a), (3,b)}
C) {(1,b), (2,b), (3,c)}
💬 Comment your answer!

📘 Chapter 3 – Sets and Functions | Part 22: Domain, Codomain & RangeIn a function f: A → B:🔹 Domain → Input values🔹 Codo...
09/08/2026

📘 Chapter 3 – Sets and Functions | Part 22: Domain, Codomain & Range
In a function f: A → B:
🔹 Domain → Input values
🔹 Codomain → Possible output values
🔹 Range → Actual output values
Example
If
f = {(1,2), (2,4), (3,6)}
and B = {2,4,6,8}
Then:
Domain = {1,2,3}
Codomain = {2,4,6,8}
Range = {2,4,6}
🧠 Quick Quiz:
If f = {(1,a),(2,b),(3,a)} and B = {a,b,c}, what is the Range?
A) {1,2,3}
B) {a,b}
C) {a,b,c}
💬 Comment your answer!

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