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Let f(x) = tan^(-1) (x^2-18x + a) gt 0 x...

Let `f(x) = tan^(-1) (x^2-18x + a) gt 0 x in R`. Then the value of a lies in

A

`(81,oo)`

B

`{81,oo)`

C

`(-oo,81)`

D

`(-oo,81]`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `f(x)=tan^(-1)(x^2-18x+a)gt0`
`rArrtan^(-1)(x^2-18x+a) gt0`
`rArrx^2-18x+agt0`
`18^2-4a gt0`
`rArr a gt 18^2/4=(18xx18)/4=81`
`rArra gt 81`
`rArr a in (81,oo)`
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