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the complete set of values of 'a' for which the function f(x)=tan(inverse)(xsq.-18x+a)>0,x belongs to R.is: ans.a belongs to (81,infinity)

the complete set of values of 'a' for which the function f(x)=tan(inverse)(xsq.-18x+a)>0,x belongs to R.is:


ans.a belongs to (81,infinity)

Grade:12

1 Answers

Gokul Joshi AskiitiansExpert-IITK
42 Points
11 years ago

Dear Umme,

 

For tan-1(x2-18x+a)>0
=> x2-18x+a>0
=> x2-18x+81-81+a>0
=> (x-9)2+a-81>0
Now (x-9)2 >= 0 (equality holds for x = 9) so for the rest i.e. (a-81) to be greater than zero for all x it should be greater than zero. => a-81>0 or a > 81

Hence a belongs to (81, inf)
  
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Gokul  Joshi





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