A function f is defined by the rule `f(x)=[1-x]+[x-1]`. discuss its continuity at `x=1`.

Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuous function at x= 1.

Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 1/2,x=1 Discuss the continuity of the function at x=1.

Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 1/2,x=1 Discuss the continuity of the function at x=1.

Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 {1/2,x=1 Discuss the continuity of the function at x=1.

Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 {1/2,x=1 Discuss the continuity of the function at x=1.

If the function defined by : f(x)={{:(2x-1", "xlt2),(a", "x=2),(x+1", "xgt2):} is continuous at x = 2, find the value of 'a'. Also discuss the continuity of f(x) at x = 3.

Show that the function f defined by f(x)=|1-x+x|, where x is any real number, is a continuous function.

Is the function f defined by f(x) = {{:(x," if "x le 1),(3," if "x gt 1):} continuous at x= 0 ? At x=1? At x=2? .

Show that the function f defined by f(x)=|1-x+x|, where x is any real number,is a continuous function.

Show that the function f defined by f(x)= |1-x+|x|| , where x is any real number, is a continuous function.