If f (x)=x-2, 2< x< 4, then - Vidyadip

MCQ

If $f (x)=\sqrt{x-2}, 2< x< 4$, then

✓
f(x) is continuous in (2, 4)
B
f(x) is discontinuous in (2, 4)
C
f(x) is continuous in (2, 4) except at x = 3
D
f(x) is discontinuous in (2, 4) except at x = 3

✓

Answer

Correct option: A.

f(x) is continuous in (2, 4)

(A)
$\lim _{x \rightarrow 3} f (x)=\lim _{x \rightarrow 3} \sqrt{x-2}=1$
$f(3)=\sqrt{3-2}=1$
$\therefore \quad \lim _{x \rightarrow 3} f (x)= f (3)$
$\therefore f (x)$ is continuous at $x=3$.
Since $3 \in(2,4)$
$\therefore f (x)$ is continuous in $(2,4)$.

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