The domain of <math> <mrow> <mi>y</mi> <mo>=</mo> <mi>c</mi> <mi>o</mi> <msup> <mrow> <mi>s</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>|</mo> <mrow> <mfrac> <mrow> <mn>2</mn> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> </mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math> is [–a, b) –{g}, then value of a + b + g = ?

-> − 1 ≤ | 2 − | x | ¯ 4 | ≤ 1 -> | 2 − | x | 4 | ≤ 1  − 1 ≤ 2 − | x | 4 ≤ 1 –4 £ 2 – |x| £ 4–6 £ – |x| £ 2–2 £ |x| £ 6|x| £ 6->x Î [–6, 6] …(1)Now, 3 – x ¹ 1And x ¹ 2 …(2)and 3 – x > 0x < 3 …(3)From (1), (2) and (3)->x Î [–6, 3] – {2}a = 6b = 3g = 2a + b + g = 11

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Ncert Solutions Maths class 12th Maths Class 12th

The domain of $y = c o s^{- 1} | \frac{2 - | x |}{4} | + {(l o g (3 - x))}^{- 1}$ is [–a, b) –{g}, then value of a + b + g = ?

Option 1 -

Option 2 -

Option 3 -

Option 4 -

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

-> $- 1 \leq | \begin{matrix} \bar{2 - | x |} & 4 \end{matrix} | \leq 1$

-> $| \frac{2 - | x |}{4} | \leq 1$

$- 1 \leq \frac{2 - | x |}{4} \leq 1$

–4 £ 2 – |x| £ 4

–6 £ – |x| £ 2

–2 £ |x| £ 6

|x| £ 6

->x Î [–6, 6] …(1)

Now, 3 – x ¹ 1

And x ¹ 2 …(2)

and 3 – x > 0

x < 3 …(3)

From (1), (2) and (3)

->x Î [–6, 3] – {2}

a = 6

b = 3

g = 2

a + b + g = 11

-> <math> <mrow> <mo>−</mo> <mn>1</mn> <mo>≤</mo> <mrow> <mo>|</mo> <mrow> <mtable> <mtr columnalign="center"> <mtd columnalign="center"> <mover accent="true"> <mrow> <mn>2</mn> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> </mrow> <mo>|</mo> </mrow> </mrow> <mo stretchy="true">¯</mo> </mover> </mtd> <mtd columnalign="center"> <mn>4</mn> </mtd> </mtr> </mtable> </mrow> <mo>|</mo> </mrow> <mo>≤</mo> <mn>1</mn> </mrow> </math> -> <math> <mrow> <mrow> <mo>|</mo> <mrow> <mfrac> <mrow> <mn>2</mn> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> </mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mo>≤</mo> <mn>1</mn> </mrow> </math>  <math> <mrow> <mo>−</mo> <mn>1</mn> <mo>≤</mo> <mfrac> <mrow> <mn>2</mn> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> </mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mo>≤</mo> <mn>1</mn> </mrow> </math> –4 £ 2 – |x| £ 4–6 £ – |x| £ 2–2 £ |x| £ 6|x| £ 6->x Î [–6, 6]              …(1)Now, 3 – x ¹ 1And x ¹ 2                    …(2)and 3 – x > 0x < 3                            …(3)From (1), (2) and (3)->x Î [–6, 3] – {2}a = 6b = 3g = 2a + b + g = 11

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The domain of $y = c o s^{- 1} | \frac{2 - | x |}{4} | + {(l o g (3 - x))}^{- 1}$ is [–a, b) –{g}, then value of a + b + g = ?

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The domain of y = c o s − 1 | 2 − | x | 4 | + ( l o g ( 3 − x ) ) − 1 is [–a, b) –{g}, then value of a + b + g = ?

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The domain of $y = c o s^{- 1} | \frac{2 - | x |}{4} | + {(l o g (3 - x))}^{- 1}$ is [–a, b) –{g}, then value of a + b + g = ?