Paragraph If f(x)= x x^2+x+1 , then On the basis of above information, answer the following : Question If f( x) d x=x- 2 3 ⁻¹(g(x))+c , then for x (- 3 , 3 ) range of g(x) is -

Step-by-step solution

aligned & x d x ( ^2 x+ x+1 ) & = x ^2 x d x (1+ ^2 x ) (1+ ^2 x+ x ) aligned Let x = t ^2 x d x=d t= t d t (1+t^2 ) (1+t^2+t ) = (1+t^2+t )- (1+t^2 ) (1+t^2 ) (1+t^2+t ) d t aligned & = dt ( t ^2+1 ) - dt (1+ t ^2+ t ) & = ⁻¹( t )- 2 3 ⁻¹ ( 2 t +1 3 ) & = x - 2 3 ⁻¹ ( 2 x +1 3 )+ c & g ( x )= 2 x +1 3 & =- 3 x 3 & - 2 3 +1 3 2 x +1 3 2 3 +1 3 & 1 3 -2 g ( x ) 1 3 +2 aligned