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If the domain is ℝ, what is the range of the function f(x) = 4x² − 1?यदि डोमेन ℝ है, तो फलन f(x) = 4x² − 1 का परास क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: [−1, ∞)[−1, ∞)
For every real x, x² ≥ 0, so f(x) = 4x² − 1 ≥ −1. The value −1 is attained at x = 0, and the function grows without bound as |x| increases. Therefore, its range is [−1, ∞).हर वास्तविक x के लिए x² ≥ 0, इसलिए f(x) = 4x² − 1 ≥ −1। x = 0 पर फलन का मान −1 होता है, और |x| बढ़ने पर फलन का मान बिना सीमा के बढ़ता है। अतः इसका परास [−1, ∞) है।
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