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The difference of maximum and minimum va...

The difference of maximum and minimum value of `(x^(2)+4x+9)/(x^(2)+9)` is

A

`1//3`

B

`2//3`

C

`-2//3`

D

`4//3`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Let `(x^(2)+4x+9)/(x^(2)+9)=y`
`implies(y-1)x^(2)-4x+9(y-1)=0`
For real value of `x`, `D ge 0`
`(5-3y)(3y-1) ge 0`
`implies (1)/(3) le y le (5)/(3)`
`:.` Difference `=(5)/(3)-(1)/(3)=(4)/(3)`
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