Find The Domain Of

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Question

Find the domain of

medium

Solution

Correct option is

f (x) (3,4)

log_1/2 (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 x 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 f (x) (3, 4) or ]3, 4[.

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