JEE Main2013MathematicsDifferentiationActual

Let f(x)= x^2-x x^2+2 x x 0,-2 . Then d d x [f⁻¹(x) ] (wherever it is defined) is equal to:

Options

A-1 (1-x)^2
B3 (1-x)^2
C1 (1-x)^2
D-3 (1-x)^2

Correct answer

B. 3 (1-x)^2

Step-by-step solution

Let y= x^2-x x^2+2 x aligned & (x^2+2 x ) y=x^2-x & x(x+2) y=x(x-1) & x[(x+2) y-(x-1)]=0 & x 0, (x+2) y-(x-1)=0 & x y+2 y-x+1=0 & x(y-1)=-(2 y+1) & x= 2 y+1 1-y f⁻¹(x)= 2 x+1 1-x & d d x (f⁻¹(x) )= 2(1-x)-(2 x+1)(-1) (1-x)^2 & = 2-2 x+2 x+1 (1-x)^2 = 3 (1-x)^2 aligned

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