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

Find the domain of the function : `f(x)=(log)_((x-4))(x^2-11 x+24)`

Text Solution

Verified by Experts

The correct Answer is:
`(8,oo)`
`f(x)=log_(x-4)(x^(2)-11x+24).`
`f(x)` is defined if
`x-4 gt 0 " and " ne 1 " and " x^(2)-11x+24 gt0`
or `x gt 4 " and " ne 5 " and " (x-3)(x-8) gt 0`
i.e., `x gt 4 " and " ne 5 " and " x lt 3 " or " x gt 8`
or ` x gt 8`
or domain`(y)=(8,oo)`
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