The domain of the function, f(x)=(√ sin x/√(x-2)(8-x)) is

Question

The domain of the function, f(x)=(√ sin x/√(x-2)(8-x)) is (A) [0, π] ∪[2 π, 8) (B) (2, π] ∪[2 π, 8) (C) (2,8) (D) (0,8)

Tardigrade Admin · Accepted Answer

(x-2)(8-x)>0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f2f6a0d387e01178632d4246d1eadb96-.png" /> sin x ≥ 0 (2, π] ∪[2 π, 8)

Q. The domain of the function, $f (x) = \frac{s i n x}{( x - 2 ) ( 8 - x )}$ is

$[0, π] \cup [2 π, 8)$

$(2, π] \cup [2 π, 8)$

$(2, 8)$

$(0, 8)$

$(x - 2) (8 - x) > 0$

$sin x \geq 0$
$(2, π] \cup [2 π, 8)$

Q. The domain of the function, f(x)=(x−2)(8−x)​sinx​​ is

[0,π]∪[2π,8)

(2,π]∪[2π,8)

(2,8)

(0,8)