Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let f(x) be a function defined by f(x) =
If f(x) is continuous at x = 1 but not at x = 2, prove that the locus of point (a, b) is a straight line excluding the point where it cuts the line y = 3.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. f(x) is continuous at x = 1 ⇔ 
f(x) = f(1) = 
f(x)
⇔ a – b = 3
f(x) is discontinuous at x = 0 ⇔ 
f(x) ≠ 
f(x) ⇔
6 ≠ 4b – a
Hence the locus of (a, b) is x – y = 3, given that 4y – x
≠ 6, i.e. y ≠ 3
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