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AP EAMCET202419 May 2024Evening ShiftMathematicsContinuity and DifferentiabilityActual

The function f(x)= array ll 2 5-x , & x 3 5-x, & x 3 array . is

Options

  1. Aleft discontinuous at x=3
  2. Bleft continuous at x=3
  3. Cright discontinuous at x=5
  4. Ddiscontinuous at x=5

Correct answer

A. left discontinuous at x=3

Step-by-step solution

Given, f(x)= cases 2 5-x , & x 3 5-x, & x 3 cases aligned & _ x 3⁻ f(x)= _ x 3⁻ 2 5-x = 2 5-3 =1 & & _ x 3⁺ f(x)= _ x 3⁺ (5-x)=2 and f(3)=5-3=2 aligned Since, _ x 3⁻ f(x) _ x 3⁺ f(x)=f(3) So, f(x) is left discontinuous at x=3 .

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