If f: R R is defined by f(x)= array cl x-1, & for x 1 2-x^2, & for 1 < x 3 x-10, & for 3 < x < 5 2 x, & for x 5 array . then the set of points of discontinuity of f is

Step-by-step solution

Given function f(x)= cases x-1, & for x 1 2-x^2, & for 1 < x 3 x-10, & for 3 < x < 5 2 x, & for x 5 cases So, f(x) will be continuous in the intervals (- , 1),(1,3),(3,5) and (5, ) Now, let us check the continuity at x=1,3 and 5 Here, (i) At x=1 , _ x 1⁻ f(x)=1-1=0 and _ x 1⁺ f(x)=2-1=1 therefore F is not continuous at x=1 (ii) aligned & At x=3, & _ x 3⁻ f(x)=2-9=-7 and & f(3)=-7 and _ x 3⁺ f(x)=3-10=-7 aligned therefore f is continuous at x=3 (iii) At x=5, _ x 5⁻ f(x)=5-10=-5 and, _ x 5⁺ f(x)=2 5=10 therefore f is