f(x) cases = 1+p x - 1-p x x & , if 1 x < 0 = 2 x+1 x-2 & , if 0 x 1 cases is continuous in the interval [-1,1] , then p =

Step-by-step solution

aligned & _ x 0⁻ f(x)= _ x 0⁻ 1+p x - 1-p x x & = _ x 0⁻¹ [( 1+p x )-( 1-p x )][( 1+p x )+( 1-p x )] x[( 1+p x )+( 1-p x )] & = _ x 0⁻ [(1+p x)-(1-p x)] x[ 1+p x + 1-p x ] = _ x 0⁻ 2 p 1+p x + 1-p x & = 2 p 2 =p & _ x 0⁺ f(x)= _ x 0⁺ 2 x+1 x-2 = 1 -2 aligned Since f ( x ) is continuous at x =0 , we get p = -1 2