For the given function, ƒ, determine if the function is discontinuous at a given point. State which condition of continuity fails or state the function is continuous at x = a.

Question

For the given function, ƒ, determine if the function is discontinuous at a given point. State which condition of continuity fails or state the function is continuous at x = a.

f(x) = 3+x,        x<0

         x,          0 is less than or equal to x is less than or equal to 1, a = 1

         x^2         x>1

Answer 1

limit of given function x approaches a

where a=1 is the value 1 ,,,,,both for x->1^- and for x->1⁺

for x=1 the function is defined f(x)=x,,,,function exists at x=1 and its value is f(1)=1

f(x) continuous at x=1 since

limit from + side of a = limit from- side of a, &

that value is the same as the function actual value at a