14. If f(x) = log (1+x),-1
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14. If f(x) = log (1+x),-1
JEE/Engineering Exams
Maths
Solution
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( fleft(frac{3 x+x^{3}}{1+3 x^{2}}right)-fleft(frac{2 x}{1+x^{2}}right) ) ( log _{0} m=operatorname{rol}_{0} frac{3 x+x^{3}}{1+3 x^{2}}-log left(frac{1+frac{2 x}{1+x^{2}}}{1-frac{2 x}{1+x^{2}}}right) ) ( log left(frac{1+3 x^{2}+3 x+x^{3}}{1+3 x^{2}-3 x-x^{3}}right)-log left(frac{1 pm x^{2}+2 x}{1+x^{2}-2 x}right) ) ( log left(frac{(1+x)^{3}}{(1-x)^{3}}right)-log left(frac{(1+x)^{2}}{(1-x)^{2}}right) ) ( 3 log left(frac{1+x}{1-x}right)-2 log left(frac{1+x}{1-x}right) ) ( =log left(frac{1+x}{1-x}right)=f(x) )

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