Question

3x + 1+x 31. If f(x) = 10967). then 14+372) is equal to (2) (fx)? (4) 24x) (3) 3(x) or nh 011 47623458

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

( begin{aligned} f(x) &=lg frac{1+x}{1-x} fleft(frac{3 x+x^{3}}{1+3 x^{2}}right) &=log frac{1+frac{3 x+x^{3}}{1+3 x^{2}}}{1-frac{3 x+x^{3}}{1+3 x^{2}}} &=log frac{1+3 x^{2}+3 x+x^{3}}{1+3 x^{2}-3 x-x^{3}} &=log frac{1+3 cdot 1^{2} x+3 cdot 1 cdot x^{2}+x^{3}}{1-3 cdot 1^{2} x+3 cdot 1 cdot x^{2}-x^{3}} &=log frac{(1+x)^{3}}{(1-x)^{3}} &=3 cdot 9-frac{1+x}{1-x} &=3 f(x) end{aligned} )