The domain of the function $$f(x)=logx+12$$⁡$$x2$$−$$5x+6$$ is

Correct option is 132,2∪(2,3)∪(3,∞)

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The domain of the function $f (x) = \log_{[x + \frac{1}{2}]} |x^{2} - 5 x + 6| is$

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32,2∪(2,3)∪(3,∞)

32,∞

12,∞

None of these

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detailed solution

Correct option is A

f (x) is defined ifx2−5x+6≠0,x+12>0,x+12≠1 x2−5x+6≠0⇒(x−2)(x−3)≠0⇒x≠2,3 ......(1) x+12>0⇒x≥12 ......(2)x+12≠1⇒x∉12,32 ......(3)From Eq. (1), (2) and (3), we get domain of f=32,2∪(2,3)∪(3,∞)

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The domain of the function f(x)=logx+12⁡x2−5x+6 is

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The domain of the function $f (x) = \log_{[x + \frac{1}{2}]} |x^{2} - 5 x + 6| is$