Maths-
General
Easy

Question

Domain of definition of the functionf left parenthesis x right parenthesis equals fraction numerator 1 over denominator 4 minus x squared end fraction plus l o g subscript 10 invisible function application open parentheses x cubed minus x close parentheses, is

  1. left parenthesis negative 10 right parenthesis union left parenthesis 12 right parenthesis union left parenthesis 2 comma infinity right parenthesis    
  2. left parenthesis 12 right parenthesis    
  3. left parenthesis negative 10 right parenthesis union left parenthesis 12 right parenthesis    
  4. left parenthesis 12 right parenthesis union left parenthesis 2 comma infinity right parenthesis    

hintHint:

Wavy curve method
The wavy curve method (also called the method of intervals) is a strategy used to solve inequalities of the form fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction greater than space 0 comma space left parenthesis less than 0 comma space less or equal than 0 comma space greater or equal than 0 right parenthesis
The method uses the fact that fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction,can only change sign at its zeroes and vertical asymptotes, so we can use the roots of blank and blankto sketch a graph of the function over different intervals.blank

The correct answer is: left parenthesis negative 10 right parenthesis union left parenthesis 12 right parenthesis union left parenthesis 2 comma infinity right parenthesis



    Given, f left parenthesis x right parenthesis equals fraction numerator 1 over denominator 4 minus x squared end fraction plus l o g subscript 10 invisible function application open parentheses x cubed minus x close parentheses,
    D o m a i n left parenthesis fraction numerator 1 over denominator 4 minus x squared end fraction right parenthesis space equals space w h o l e space R space e x c e p t left parenthesis negative 2 comma 2 right parenthesis ....... (1)
    log subscript 10 open parentheses x cubed minus x close parentheses space w i l l space b e space w e l l space d i e f i n e d space i f space x cubed space minus x space greater than 0
    rightwards double arrowx(x-1)(x+1) > 0
     By wavy curve method


    When x> 1, function is positive
    When x lies between 0 and 1, function is negative
    When x lies between -1 and 0, function is positive
    When x lies between < -1 , function is negative
    T h u s comma space d o m a i n space for all x space element of left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma infinity right parenthesis space..... space left parenthesis 2 right parenthesis

T h u s comma space d o m a i n space o f space d e f i n i t i o n space left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis

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