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Maths-

General

Easy

Question

The domain of the function $square root of 1 minus f left parenthesis x right parenthesis end root text where end text f to the power of 3 end exponent left parenthesis x right parenthesis equals 1 minus x to the power of 3 end exponent minus 3 x f left parenthesis x right parenthesis. x element of R text is end text left parenthesis f left parenthesis 1 right parenthesis not equal to negative 1 right parenthesis$

R
$R - {0}$
$R^{+} \cup {0}$
$R^{-}$

The correct answer is: $R to the power of plus end exponent union left curly bracket 0 right curly bracket$

$table row cell left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of 3 end exponent plus left parenthesis x right parenthesis to the power of 3 end exponent plus left parenthesis negative 1 right parenthesis to the power of 3 end exponent minus 3 left parenthesis negative 1 right parenthesis left parenthesis x right parenthesis left parenthesis f left parenthesis x right parenthesis right parenthesis equals 0 end cell row cell rightwards double arrow open parentheses f open parentheses x close parentheses plus x plus open parentheses negative 1 close parentheses close parentheses open parentheses f to the power of 2 end exponent left parenthesis x right parenthesis plus x to the power of 2 end exponent plus left parenthesis negative 1 right parenthesis to the power of 2 end exponent minus x f left parenthesis x right parenthesis plus x plus f left parenthesis x right parenthesis close parentheses equals 0 end cell row cell text end text text U end text text s end text text i end text text n end text text g end text text end text a to the power of 3 end exponent plus b to the power of 3 end exponent plus c to the power of 3 end exponent minus 3 a b c equals left parenthesis a plus b plus c right parenthesis open parentheses a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent minus a b minus b c minus c a close parentheses end cell row cell f to the power of 2 end exponent left parenthesis x right parenthesis plus x to the power of 2 end exponent plus left parenthesis negative a right parenthesis to the power of 2 end exponent minus x f left parenthesis x right parenthesis plus x plus f left parenthesis x right parenthesis end cell row cell equals fraction numerator 1 over denominator 2 end fraction open curly brackets left parenthesis f left parenthesis x right parenthesis minus x right parenthesis to the power of 2 end exponent plus left parenthesis x plus 1 right parenthesis to the power of 2 end exponent plus left parenthesis f left parenthesis x right parenthesis plus 1 right parenthesis to the power of 2 end exponent close curly brackets greater or equal than 0 end cell end table$
$table row cell text end text text E end text text q end text text u end text text a end text text l end text text i end text text t end text text y end text text end text text o end text text c end text text c end text text u end text text r end text text s end text text end text text a end text text t end text text end text f left parenthesis x right parenthesis equals x equals negative 1 rightwards double arrow f left parenthesis 1 right parenthesis equals negative 1 end cell row cell text end text text B end text text u end text text t end text text end text text i end text text t end text text end text text i end text text s end text text end text text g end text text i end text text v end text text e end text text n end text text end text text t end text text h end text text a end text text t end text text end text f left parenthesis 1 right parenthesis not equal to negative 1 end cell row cell text end text text O end text text n end text text l end text text y end text text end text text s end text text o end text text l end text text u end text text t end text text i end text text o end text text n end text text end text text i end text text s end text text end text f left parenthesis x right parenthesis equals 1 minus x end cell row cell text end text text d end text text o end text text m end text text a end text text i end text text n end text text end text text o end text text f end text text end text square root of 1 minus f open parentheses x close parentheses end root equals square root of x text end text text i end text text s end text text end text x element of R to the power of plus end exponent union left curly bracket 0 right curly bracket end cell end table$

Related Questions to study

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i) All solution produce carbonate precipitate with (NH₄)₂CO₃
ii) Only one produce white ppt on addition of NaCl.
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
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