Domain of the function fx-sin -11-3 x-2 x2 isA- -1-1B- -3-2- 0-C- - -1-2 -2- -D- - -

The correct option is B 1≤1+3x+2x^3≤ 1 Case | : 2x^3+3x+1≥ 1;2x^3+3x+2≥ 0 x= 3±√(9 16)/6= 3± i√(7)/6 (imaginary). Case || : 2x^3+3x+1≤ 1 ⇒ 2x^2+3x≤ 0 ∴ 2x(x ...

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Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

Domain of the...

Question

Domain of the function $f (x) = s i n^{- 1} (1 + 3 x + 2 x^{2})$ is

( -∞, ∞)

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( -1 , 1)

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Solution

The correct option is C

$- 1 \leq 1 + 3 x + 2 x^{3} \leq 1$

Case | : $2 x^{3} + 3 x + 1 \geq - 1; 2 x^{3} + 3 x + 2 \geq 0$

$x = \frac{- 3 \pm \sqrt{9 - 16}}{6} = \frac{- 3 \pm i \sqrt{7}}{6}$ (imaginary).

Case || : $2 x^{3} + 3 x + 1 \leq 1$

$\Rightarrow 2 x^{2} + 3 x \leq 0 ∴ 2 x (x + \frac{3}{2} \leq 0)$

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Domain of the function f(x)=sin−1(1+3x+2x2) is

The correct option is C −1≤1+3x+2x3≤ 1 Case | : 2x3+3x+1≥ −1;2x3+3x+2≥ 0 x=−3±√9−166=−3± i√76 (imaginary). Case || : 2x3+3x+1≤ 1 ⇒ 2x2+3x≤ 0 ∴ 2x(x+32≤ 0)

Domain of the function $f (x) = s i n^{- 1} (1 + 3 x + 2 x^{2})$ is