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Question

The solution of the inequality open parentheses tan to the power of negative 1 end exponent invisible function application x close parentheses to the power of 2 end exponent minus 3 t a n to the power of negative 1 end exponent invisible function application x plus 2 greater or equal than 0 text  is - end text

  1. left parenthesis negative infinity comma t a n invisible function application 1 right square bracket union left square bracket t a n invisible function application 2 comma infinity right parenthesis    
  2. left parenthesis negative infinity comma t a n invisible function application 1 right square bracket    
  3. left parenthesis negative infinity comma negative t a n invisible function application 1 right square bracket union left square bracket t a n invisible function application 2 comma infinity right parenthesis    
  4. left square bracket t a n invisible function application 2 comma infinity right parenthesis    

hintHint:

take, tan-1(x) as t now the inequality will be converted into a simple quadratic inequality

The correct answer is: left parenthesis negative infinity comma t a n invisible function application 1 right square bracket


    let tan-1(x) = t
    n o w space t h e space e q u a t i o n space w o u l d space b e thin space colon
t squared plus negative 3 t space plus space 2 space greater than equals 0
t squared space minus 2 t space minus t space plus 2 space greater than equals 0 space space left parenthesis s p i t t i n g space t h e space m i d d l e space t e r m right parenthesis
t space left parenthesis t minus 2 right parenthesis space minus 1 space left parenthesis t minus 2 right parenthesis space greater than equals 0 space left parenthesis t a k i n g space c o m m o n right parenthesis space
left parenthesis t minus 1 right parenthesis space left parenthesis t minus 2 right parenthesis space greater than equals 0 space
t element of left parenthesis negative infinity comma 1 right square bracket space U space left parenthesis 2 comma infinity right square bracket
b u t space t space equals space tan to the power of negative 1 end exponent left parenthesis x right parenthesis
tan to the power of negative 1 end exponent left parenthesis x right parenthesis element of space left parenthesis negative infinity comma 1 right square bracket space U space left parenthesis 2 comma infinity right square bracket

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