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AP EAMCET202021 Sep 2020Morning ShiftMathematicsContinuity and DifferentiabilityActual

(f(x)= array cc x-4 |x-4| +a, & x 4 array . ) If (f(x) ) given above is continuous at (x=4 ), then find the values of ' (a ) ' and ' (b ) '.

Options

  1. A(a=1, b=-1 )
  2. B(a=-1, b=1 )
  3. C(a=1, b=1 )
  4. D(a=-1, b=-1 )

Correct answer

A. (a=1, b=-1 )

Step-by-step solution

Given function ( aligned f(x) & = [ array cc x-4 |x-4| +a, & x 4 array . & = [ array cl -1+a, & x 4 array . aligned ) ( ) Function (f ) is continuous at (x=4 ), so LHL (at (x=4)=f(4)= ) RHL (at (x=4 )) ( -1+a=a+b=1+b a=1 ) and (b=-1 ) Hence, option (a) is correct.

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