The domain of the function f(x)= sin -1((x2-3 x+2/x2+2 x+7)) is :

Question

The domain of the function f(x)= sin -1((x2-3 x+2/x2+2 x+7)) is : (A) [1, ∞) (B) (-1,2] (C) [-1, ∞) (D) (-∞, 2]

Tardigrade Admin · Accepted Answer

f(x)= sin -1((x2-3 x+2/x2+2 x+7)) Domain (x2-3 x+2/x2+2 x+7) ≥-1 and (x2-3 x+2/x2+2 x+7) ≤ 1 2 x2-x+9 ≥ 0 and 5 x ≥-5 ⇒ x ≥-1 x ∈ R Hence Domain x ∈[-1, ∞)

Q. The domain of the function $f (x) = sin^{- 1} (\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7})$ is :

$[1, \infty)$

$(- 1, 2]$

$[- 1, \infty)$

$(- \infty, 2]$

$f (x) = sin^{- 1} (\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7})$
Domain $\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7} \geq - 1$
and $\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7} \leq 1$
$2 x^{2} - x + 9 \geq 0$
and $5 x \geq - 5 \Rightarrow x \geq - 1$ $x \in R$
Hence Domain $x \in [- 1, \infty)$

Q. The domain of the function f(x)=sin−1(x2+2x+7x2−3x+2​) is :

[1,∞)

(−1,2]

[−1,∞)

(−∞,2]