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# Find The Domain Of

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## Question

### Solution

Correct option is

(x (3,4)

log1/2 (x2 – 7x + 13) > 0

⇒             (x2 – 7x + 13) < 1                … (i)

And           x2 – 7x + 13 > 0                 … (ii)

Considering equation (ii), x2 – 7x + 13 > 0, we have

Which is true for all  R

again taking (i) x2 – 7x + 13 < 1

⇒        x2 – 7x + 12 < 0

⇒       (x – 3) (x – 4) < 0

⇒        3 < x < 4                           … (b)

Combining (a) and (b), we have

Hence, domain of (x (3, 4)   or   ]3, 4[.

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