Question
Download Solution PDFIf the function \(\rm {f}(\mathbf{x})=\left\{\begin{array}{cc} 1, & x \leq 2 \\ a x+b, & 2<x<4 \\ 7, & x \geq 4 \end{array}\right.\) is continuous at x = 2 and 4, then the values of a and b are.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Since f(x) is continuous at x=2
∴ f(2) = \(\lim_{x\rightarrow2}\) f(x) = 1 = \(\lim_{x\rightarrow2}\) (ax+b)
∴ 1 = 2a + b ... (i)
Again f(x) is continuous at x=4,
∴ f(4) = \(\lim_{x\rightarrow4}\) f(x) = 7 = \(\lim_{x\rightarrow4}\) (ax+b)
∴ 7 = 4a + b ... (ii)
Solving (i) and (ii), we get a = 3, b = -5
Hence option 1 is correct
Last updated on Jul 3, 2025
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