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Show that the function f(x)=(4 - x^2)/(3 - square root of blank end rootx^2 +5)      has removable discontinuity at x=2
and x=-2
 
the function is 4 minus x square divided by 3 - square root of x square + 5

Asked by ahuja8087 7th July 2016, 12:10 AM
Answered by Expert
Answer:
f left parenthesis x right parenthesis space equals space fraction numerator open parentheses 4 minus x squared close parentheses over denominator open parentheses 3 minus square root of x squared plus 5 end root close parentheses end fraction
f left parenthesis x right parenthesis space equals space fraction numerator open parentheses 4 minus x squared close parentheses over denominator open parentheses 3 minus square root of x squared plus 5 end root close parentheses end fraction cross times fraction numerator 3 plus square root of x squared plus 5 end root over denominator 3 plus square root of x squared plus 5 end root end fraction
f left parenthesis x right parenthesis equals fraction numerator open parentheses 4 minus x squared close parentheses open square brackets 3 plus square root of x squared plus 5 end root close square brackets over denominator open parentheses 3 close parentheses squared minus open parentheses square root of x squared plus 5 end root close parentheses squared end fraction
f left parenthesis x right parenthesis equals fraction numerator open parentheses 4 minus x squared close parentheses open square brackets 3 plus square root of x squared plus 5 end root close square brackets over denominator 9 minus x squared minus 5 end fraction
f left parenthesis x right parenthesis equals fraction numerator open parentheses 4 minus x squared close parentheses open square brackets 3 plus square root of x squared plus 5 end root close square brackets over denominator open parentheses 4 minus x squared close parentheses end fraction
f left parenthesis x right parenthesis space equals space 3 plus square root of x squared plus 5 end root

From space above space we space can space see space that space space the space factor space open parentheses 4 minus straight x squared close parentheses space got space cancelled space from space numerator space and space denominator.
So space open parentheses 4 minus straight x squared close parentheses space equals space 0 space is space the space removable space discontinuity space of space straight f left parenthesis straight x right parenthesis space
That space is space straight x space equals space plus-or-minus 2 space is space the space removable space discontinuity space of space straight f left parenthesis straight x right parenthesis.
Answered by Expert 7th July 2016, 2:40 PM
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