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The number of integers in the domain of function, satisfying `f(x)+f(x^(-1))=(x^3+1)/x ,i s_____` |
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Answer» Correct Answer - 2 `f(x)+f((1)/(x))=x^(2)+(1)/(x)` Replacing x by `(1)/(x),` we get `f((1)/(x))+f(x)=(1)/(x^(2))+x` `or (1)/(x^(2))+x=x^(2)+(1)/(x)` `or x-(1)/(x)=x^(2)-(1)/(x^(2))` `or (x-(1)/(x))=(x-(1)/(x))(x+(1)/(x))` ` or (x-(1)/(x))(x+(1)/(x)-1)=0` `x=(1)/(x), x+(1)/(x)=1`(rejected) Hence, `x=1 or -1.` |
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