InterviewSolution
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InterviewSolution
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Which of the following functions has (have) y-symmetry or origin symmetry? (i) ` f(x) = x^(2) sin x" "(ii) f(x) = log ((1-x)/(1+x))` (iii)` f(x) = x/(e^(x)-1)+x/2 + 1` |
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Answer» (i) `f(-x) = (-x)^(2) sin (-x) =- x^(2) sin x =- f(x)`, hence the function has origin symmetry (ii) `f(-x)= log((1-(-x))/(1+(-x))) = log ((1+x)/(1-x))=- f(x)`hence the function has origin symmetry (iii) `f(x) = x/(e^(x)-1)+x/2 + 1` ` rArr f(-x) = (-x)/(e^(-x)-1)-x/2 + 1` ` = (xe^(x))/(e^(x)-1) - x/2 + 1` `=(xe^(x)-x+x)/(e^(x)-1) - x/2+1` ` = x+x/(e^(x)-1)-x/2 + 1` ` = x/(e^(x)-1) + x/2 + 1` = f(x) Hence the function has y-symmetry. |
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