The value (s) of x for which the function f(x)= array cc 1-x, & x 2 array . fails to be continuous is(are)

Step-by-step solution

Given function, f(x)= array cc 1-x, & x 2 array . For f(x) to be continuous at x=1 . aligned & _ x 1⁺ f(x)= _ x 1⁺ f(x)=f(1) & _ x 1⁺ (1-x)= _ x 1⁺ (1-x)(2-x) & (1-1)=(1-1)(2-1)=0 aligned and f(1)=(1-1)(2-1)=0 f(x) is continuous at x=1 . Now, at x=2, _ x 2⁻ f(x)= _ x 2⁻ f(x)=f(2) aligned & _ x 2⁻ (1-x)(2-x)= _ x 2⁺ (3-x) & (1-2)(2-2)=(3-2) & 0 1 & f(x) is discontinuous at x=2 aligned f(x) is discontinuous at x=2 .