Examine the continuity of the following function at the given point : `f(x) = {(x^2 - 2x + 3, x < 1),(2, x = 1),(2x^2 - 5x + 5, x > 1):}` x = 1.

Examine the continuity of the following function at the given point : f(x) = {(1 + x, x 0),(1, x = 0):} at x = 0.

Examine the continuity of the following function at the given point : f(x) = {(x, 0 le x < 1/2),(1, x = 1/2),(1-x, 1/2 < x < 1):} at x = 1/2 .

Examine the continuity of the following function at the given point : f(x) ={((3/2-x, 1/2 le x < 1)),((3/2, x = 1)),((3/2 + x, 1 < x le 2)):} at x = 1.

Find the range of the following functions given by : f(x)=3/(2-x^2)

Find the range of the following functions given by : f(x)=|x-3|

Find the range of the following functions given by : f(x)=1-|x-2|

Find the domain of the following functions given by f(x)=(x^2+2x+1)/(x^2-4) .

Find the range of the following functions given by : f(x)=|x-2|/(x-2) .

Find the domain of the following functions given by f(x)=x|x| .

Examine continuity of the function f defined by. f(x)=x-5