Which of the following functions is not defined for all real values of its variable?
Advertisement
Answer and explanation
Correct answer: \(\tan x\)
\(\tan x=\frac{\sin x}{\cos x}\). For \(x=\frac{(2n+1)\pi}{2}\), \(\cos x=0\), so \(\tan x\) is undefined. In contrast, \(\sin x\) and \(\cos x\) are defined for every real \(x\). Exam tip: for a quotient function, first check where its denominator becomes zero.
Frequently asked questions
What is the correct answer to this question?
\(\tan x\)
Why is this the correct answer?
\(\tan x=\frac{\sin x}{\cos x}\). For \(x=\frac{(2n+1)\pi}{2}\), \(\cos x=0\), so \(\tan x\) is undefined. In contrast, \(\sin x\) and \(\cos x\) are defined for every real \(x\). Exam tip: for a quotient function, first check where its denominator becomes zero.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
Advertisement