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Which of the following functions is even?निम्न में से कौन-सा फलन सम है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\cos x\)\(\cos x\)
For an even function, \(f(-x)=f(x)\) for every value in its domain. Since \(\cos(-x)=\cos x\), \(\cos x\) is an even function. In contrast, \(\sin x\), \(\tan x\), and \(\cot x\) are odd functions because they satisfy \(f(-x)=-f(x)\). Exam tip: an even function is symmetric about the \(y\)-axis.सम फलन के लिए प्रत्येक परिभाषित मान पर \(f(-x)=f(x)\) होना चाहिए। क्योंकि \(\cos(-x)=\cos x\), इसलिए \(\cos x\) सम फलन है। इसके विपरीत, \(\sin x\), \(\tan x\) और \(\cot x\) विषम फलन हैं, क्योंकि इनके लिए \(f(-x)=-f(x)\) होता है। परीक्षा टिप: सम फलन सामान्यतः \(y\)-अक्ष के सापेक्ष सममित होता है।
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