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Maths-

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Question

If $f left parenthesis x right parenthesis equals s i n to the power of negative 1 end exponent invisible function application x text and end text g left parenthesis x right parenthesis equals left square bracket s i n invisible function application x left parenthesis c o s invisible function application x right parenthesis right square bracket plus left square bracket c o s invisible function application left parenthesis s i n invisible function application x right parenthesis right square bracket comma text end text$ then range of f(g(x)) is

$\{- \frac{π}{2}, \frac{π}{2}\}$
$\{- \frac{π}{2}, 0\}$
$\{0, \frac{π}{2}\}$
$\{- \frac{π}{2}, 0, \frac{π}{2}\}$

The correct answer is: $open curly brackets negative fraction numerator pi over denominator 2 end fraction comma 0 comma fraction numerator pi over denominator 2 end fraction close curly brackets$

$table row cell negative 1 less or equal than cos invisible function application x less or equal than 1 end cell row cell negative sin invisible function application 1 less or equal than sin invisible function application open parentheses cos invisible function application x close parentheses less or equal than sin invisible function application 1 end cell row cell rightwards double arrow open square brackets sin invisible function application open parentheses cos invisible function application x close parentheses close square brackets equals 0 comma negative 1 end cell row cell negative 1 less or equal than sin invisible function application x less or equal than 1 rightwards double arrow cos invisible function application 1 less or equal than cos invisible function application open parentheses sin invisible function application x close parentheses less or equal than 1 end cell row cell left square bracket c o s invisible function application x left parenthesis s i n invisible function application x right parenthesis right square bracket equals 01 end cell row cell rightwards double arrow open square brackets sin invisible function application open parentheses cos invisible function application x close parentheses close square brackets plus open square brackets cos invisible function application open parentheses sin invisible function application x close parentheses close square brackets equals negative 10 comma 1. end cell end table$

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iii) Out of 3 cations two produce sulphide ppt.
iv) Sulphide of y⁺² is not produce by H₂S/H⁺but produce when H₂S is passed in basic medium.
v) Only y⁺² produce soluble sulphate
vi) x ⁺² gives no ppt with dil NH₄OH
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ii) Only one produce white ppt on addition of NaCl.
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