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if f(x) = -1, x<0 0, x=0 1, x>0 and g(x) = x(1 - xsquare) then f(g(x)) is continuous for a R b R - {0} c R - {0,1} d R - {-1,0,1}

if f(x) = -1, x<0


             0, x=0


             1, x>0


and g(x) = x(1 - xsquare) 


then f(g(x)) is continuous for 


a R


b R - {0}


c R - {0,1}


d R - {-1,0,1}

Grade:12

1 Answers

AskIitian Expert Chaitanya
16 Points
13 years ago

Dear iit jee ,
 
G(x) = x(1-x^2)
 
       
G(x ) > 0  when  - infinity < x < -1 &  0 < x < 1
      = 0  when  x = -1 & 1
      < 0  when  -1 < x < 0  &  1 < x < infinity


Hence fog(x) = -1  when - infinity < x < -1 &  0 < x < 1
           
             =  0  when  x = -1 & 1
            
             =  1  when -1 < x < 0  &  1 < x < infinity

 hence the function is discontinous at -1 ,0,1
 

      
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Chaitanya Sagar


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