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InterviewSolution
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Discuss the continuity of the function `f(x)={{:(2x -1 "," x lt 1),(3x-2"," x ge 1):}` |
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Answer» When `x lt 1` f(x)= 2x-1 is a polynomial function `therefore` f(x) is continuous in `x lt 1` When `x gt 1` f(x) =3x -2 is a polynominal function `there` f(x) is continous in `x gt 1` At x=1 L.H.L `=underset(xrarr1^-)lim f(x)=underset(hrarr0)limf(0-h)` `=underset(xrarr0)lim2(1-h)-1=2-1=1` R. H.L `=underset(xrarr1^+)lim f(x)=underset(hrarr0)limf(1+h)` `=underset(h rarr0)lim 3(1+h) -2=3-2=1` and f(1)=`3 xx1 -2 =1` `therefore underset(x rarr 1^+)f(x) = f(1)=underset(x rarr 1^(-1))lim f(x)` `therefore` f(x) is continuous at x=1 Therefore f(x) is a continuous function . |
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