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AP EAMCET201920 Apr 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let (f: R R ) be the function defined by (f(x)= array cl 5, & if x 1 a+b x, & if 1 < x < 3 b+5 x, & if 3 x < 5 30, & if x 5 array . ) then (f ) is

Options

  1. Acontinuous if (a=5 ) and (b=5 )
  2. Bcontinuous if (a=0 ) and (b=5 )
  3. Ccontinuous if (a=-5 ) and (b=10 )
  4. Dnot continuous for any values of (a ) and (b )

Correct answer

D. not continuous for any values of (a ) and (b )

Step-by-step solution

Given function (f: R R ), such that (f(x)= [ array cl 5, & if x 1 a+b x, & if 1 < x < 3 b+5 x, & if 3 x < 5 30, & if x 5 array . ) If (f ) is continuous at (x=1 ), then (a+b=5 ) ...(i) If (f ) is continuous at (x=3 ), then ( gathered a+3 b=b+15 a+2 b=15 (ii) gathered ) and if (f ) is continuous at (x=5 ), then (b+25=30 b=5 ) ...(iii) From Eqs. (ii) and (iii), we get (a=5 ) ...(iv) but (a=5 ) and (b=5 ) doesn't satisfy the Eq. (i). so, (f: R R ) is not continuous for any values of (a ) and (b ). Hence, option (4) is

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