JEE · Maths · Relations, Functions & Inverse Trigonometry doubts
12 doubts found
Why can some functions be inverted while others can't?
An inverse must send each output back to exactly one input, so the original function has to be bijective — one-one (no two inputs share an output) and onto (every target value is reached).
Why is sin⁻¹(1/2) just π/6 and not the infinitely many angles that also have sine 1/2?
Sine is many-one — countless angles share the same sine — so a plain 'inverse' wouldn't be a function (one input, many outputs).
How do composite functions f(g(x)) work, and why does the order of composition matter?
A composite applies one function to the result of another: f(g(x)) means first do g, then feed its output into f.
What does “Bijective functions” actually mean in Relations, Functions & Inverse Trigonometry, and why does it matter for JEE?
a function has an inverse only if it is bijective — both one-one (injective) and onto (surjective).
I keep getting “Bijective functions” questions wrong in Relations, Functions & Inverse Trigonometry. What's the trap?
trying to invert a function that maps two inputs to the same output.
What does “Principal value branch” actually mean in Relations, Functions & Inverse Trigonometry, and why does it matter for JEE?
inverse trig functions are made single-valued by restricting their range to a principal branch (e.g. sin⁻¹ to [−π/2, π/2]).
I keep getting “Principal value branch” questions wrong in Relations, Functions & Inverse Trigonometry. What's the trap?
giving all possible angles instead of the principal value.
What is the difference between one-one (injective) and onto (surjective)?
One-one means different inputs give different outputs (no output repeats); onto means every element of the codomain is actually hit. A function needs both (bijective) to be invertible.
What is the difference between sin⁻¹ range and cos⁻¹ range?
sin⁻¹ returns angles in [−π/2, π/2]; cos⁻¹ returns angles in [0, π] — different principal branches chosen to keep each single-valued.
How is Relations, Functions & Inverse Trigonometry tested in JEE, and what should I focus on?
Prioritise the core ideas: Bijective functions, Principal value branch.
What are the most common mistakes students make in Relations, Functions & Inverse Trigonometry?
only bijective (one-one and onto) functions are invertible; many-one functions must have their domain restricted first.
How do I revise Relations, Functions & Inverse Trigonometry quickly before the exam?
One-page summary of Bijective functions, Principal value branch, then timed previous-year questions.