Function f(x) = begincases x - 1, x

Question

Function f(x) = begincases x - 1, x < 2 2x - 3 , x ≥ 2 endcases is continuous function: (A) for x = 2 only. (B) for all real value of x such that x ≠ 2. (C) for all real value of x. (D) for all integral value of x only.

Tardigrade Admin · Accepted Answer

Note: A polynomial function is always a continuous function. And the given question is a polynomial function with degree 1. Thus the continuity is for all real value of x.

Q. Function $f (x) = {x - 1, 2 x - 3, x < 2 x \geq 2$ is continuous function:

for $x = 2$ only.

for all real value of x such that $x \neq = 2$ .

for all real value of x.

for all integral value of x only.

Note: A polynomial function is always a continuous function.
And the given question is a polynomial function with degree 1.
Thus the continuity is for all real value of x.

Q. Function f(x)={x−1,2x−3,​x<2x≥2​ is continuous function:

for x=2 only.

for all real value of x such that x=2.