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The function `f(x)=(x+1)/(x^3+1)`can be written as the sum of an even function `g(x)`and an odd function `h(x)`. Then the value of `|g(0)|`is___________ |
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Answer» `g(x)=(f(x)+f(-x))/(2)` `=(1)/(2)[(x+1)/(x^(3)+1)+(1-x)/(1-x^(3))]` `=(1)/(2)[(1)/(x^(2)-x+1)+(1)/(1+x+x^(2))]` `=(1)/(2)[(2(x^(2)+1))/((x^(2)+1)^(2)-x^(2))]` `=(x^(2)+1)/(x^(4)+x^(2)+1)` ` :. g(0)=1` |
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