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If `f(x)`is an even function and satisfies the relation `x^2dotf(x)-2f(1/x)=g(x),w h e r eg(x)`is an odd function, then find the value of `f(5)dot` |
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Answer» `x^(2)f(x)-2f((1)/(x))=g(x) " and " 2f((1)/(x))-4x^(2)f(x)=2x^(2)g((1)/(x))` or `-3x^(2)f(x)=g(x)+2x^(2)g((1)/(x))` or ` f(x)=((g(x)+2x^(2)g((1)/(x)))/(3x^(2)))` Since g(x) is odd `f(-x)= -f(x).` But given that `f(x)` is even. ` :. f(x)=0` ` :. f(5)=0` |
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