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If \(f(x)=2x^2-1\), what is the value of \((3f)(x)\)?यदि \(f(x)=2x^2-1\) है, तो \((3f)(x)\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(6x^2-3\)\(6x^2-3\)
The scalar multiple of a function is defined by \((3f)(x)=3f(x)\). Hence, \((3f)(x)=3(2x^2-1)=6x^2-3\). Option B is incorrect because multiplying the entire function by 3 changes \(-1\) to \(-3\). Exam tip: do not confuse \((3f)(x)\) with \(f(3x)\); the former multiplies the whole function by 3.किसी फलन का अदिश गुणज \((3f)(x)=3f(x)\) होता है। इसलिए \((3f)(x)=3(2x^2-1)=6x^2-3\)। विकल्प B गलत है क्योंकि 3 से \(-1\) को गुणा करने पर \(-3\) प्राप्त होना चाहिए। परीक्षा-टिप: \((3f)(x)\) को \(f(3x)\) न समझें; पहले में पूरे फलन का 3 से गुणन होता है।
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