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Find the domain of the function : f(x)=1...

Find the domain of the function : `f(x)=1/(sqrt((log)_(1/2)(x^2-7x+13)))`

Text Solution

Verified by Experts

The correct Answer is:
`(3,4)`
`f(x)=(1)/(sqrt(log_(1//2)(x^(2)-7x+13)))` exists if
`log_(1//2)(x^(2)-7x+13) gt 0`
or `x^(2)-7x+13 lt 1 " (1) " `
and `x^(2)-7x+13 gt 0 " (2)" `
or `x^(2)-7x+12 lt 0 " and " (x-(7)/(2))^(2)+(3)/(4) gt 0`
or `3 lt x lt 4 " and " x in R`
or ` 3 lt x lt 4`
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