Question
Download Solution PDFयदि फलन \(\rm {f}(\mathbf{x})=\left\{\begin{array}{cc} 1, & x \leq 2 \\ a x+b, & 2 x = 2 और 4 पर संतत है, तो a और b के मान हैं।
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चूँकि f(x), x=2 पर संतत है
∴ f(2) = \(\lim_{x\rightarrow2}\) f(x) = 1 = \(\lim_{x\rightarrow2}\) (ax+b)
∴ 1 = 2a + b ... (i)
पुनः f(x), x=4 पर संतत है,
∴ f(4) = \(\lim_{x\rightarrow4}\) f(x) = 7 = \(\lim_{x\rightarrow4}\) (ax+b)
∴ 7 = 4a + b ... (ii)
(i) और (ii) को हल करने पर, हमें a = 3, b = -5 प्राप्त होता है
इसलिए विकल्प 1 सही है
Last updated on Jul 3, 2025
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