Question

Determine the value of k so that the function

$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight x squared minus 9 over denominator straight x minus 3 end fraction comma space straight x not equal to 1 end cell row cell space space space space space space straight k space space space space space comma space straight x equals 3 end cell end table close$

Solution

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight x squared minus 9 over denominator straight x minus 3 end fraction comma space straight x not equal to 1 end cell row cell space space space space space space straight k space space space space space comma space straight x equals 3 end cell end table close space Lt with straight x rightwards arrow 3 below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 3 below fraction numerator straight x squared minus 9 over denominator straight x minus 3 end fraction equals Lt with straight x rightwards arrow 3 below fraction numerator left parenthesis straight x minus 3 right parenthesis left parenthesis straight x plus 3 right parenthesis over denominator straight x minus 3 end fraction equals Lt with straight x rightwards arrow 3 below left parenthesis straight x plus 3 right parenthesis equals 3 plus 3 equals 6 Since space straight f left parenthesis straight x right parenthesis space is space continous space at space straight x equals 3 therefore space straight f left parenthesis 3 right parenthesis equals Lt with straight x rightwards arrow 3 below straight f left parenthesis straight x right parenthesis space rightwards double arrow space straight k equals 6

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