FUN011 · Functions & graphs · Classes 10–12
Square Root Function
The square root function is half of a sideways parabola. It starts at the origin and rises ever more slowly.
√xSquare Root Function
📐 Formula
f(x) = a√x, domain x ≥ 0
✏️ Worked example
a = 1, x = 4: f(4) = √4 = 2.
🌍 Where it is used
Pendulum period (T ∝ √L), stopping distances, side of a square from its area.
❓ Quick check
What is the domain of y = √x?
🏋️ Practice
Easy√25 = ?
Answer: 5
MediumFor f(x) = 3√x, find f(16).
Answer: 12
ChallengeWhich is the inverse of f(x) = √x on x ≥ 0?
Answer: x², for x ≥ 0