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The domain of the function f(x)=1/(sqrt(...

The domain of the function `f(x)=1/(sqrt(4x-|x^2-10 x+9|))` is (a)`(7-sqrt(40),7+sqrt(40))`(b) `(0,7+sqrt(40))`(c)`(7-sqrt(40),oo)` (d) none of these

A

`(7-sqrt(40), 7+sqrt(40))`

B

`(0,7+sqrt(40))`

C

`(7-sqrt(40),oo)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=(1)/(sqrt(4x-|x^(2)-10x+9|))`
For `f(x)` to be defined , `|x^(2)-10x+9| lt 4x`
or ` x^(2)-10x +9 lt 4x " and " x^(2)-10x+9 gt -4x`
or ` x^(2)-14x +9 lt 0 " and " x^(2) -6x+9 gt 0`
or ` x in (7-sqrt(40), 7 + sqrt(40)) " and " x in R -{3}`
or ` x in (7-sqrt(40), 3) cup (3,7+sqrt(40))`
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