If f (a )= log ⁡ ( 1-a1+a ) for a -1 ,1 , then the set of values of all ' a ', for which f ( 2a1+a^2 )0 is

Question

If f (a )= log ⁡ ( 1-a1+a ) for a -1 ,1 , then the set of values of all ' a ', for which f ( 2a1+a^2 )>0 is

Accepted Answer

Correct answer: B. (b) Given f (a )= log ⁡ ( 1-a1+a ) ,a -1 ,1 Now f ( 2a1+a^2 )>0 ⇒ log ⁡ ( 1- 2a1+a^21+ 2a1+a^2 )>0 ⇒ ( 1+a^2-2a1+a^2+2a )>1 ⇒ ( (1-a )^2 (1+a )^2 )>1 ⇒ (1-a )^2- (1+a )^2 (1+a )^2>0 or (1-a^2)+(1+a^2)(1+a^2)<0 ⇒-2a>0 or 1+a^2<0 ⇒a<0 Since (1+a^2)>0 ∀a \&a 1 ) So a ∈ (- ,0 )- -1

$If f (a) = log (\frac{1 - a}{1 + a}) for a \neq = -1, 1, then the set of values of all ' a', for which f (\frac{2 a}{1 + a ^{2}}) > 0 is$

Solution

More Continuity & Differentiability PYQs