KCET2026MathematicsContinuity and Differentiability

If f(x) = cases ax + 7 & if x 1 cases is continuous at x = 1 , then

Options

Aa = -5, b = 2
Ba = -5, b = -2
Ca = 5, b = -2
Da = -5, b = 8

Correct answer

D. a = -5, b = 8

Step-by-step solution

For the function to be continuous at x = 1 , the left-hand limit, right-hand limit, and the value of the function at x = 1 must be equal. f(1) = 3(1) - 1 = 2 _ x 1⁻ f(x) = _ x 1⁻ (ax + 7) = a + 7 _ x 1⁺ f(x) = _ x 1⁺ b x + 3 = b 4 Equating these values: a + 7 = 2 a = -5 b 4 = 2 b = 8 Answer: a = -5, b = 8

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