Find the sum of integers in domain of function f(x) = \sqrt{\left(\right. 6 x - 8 - x^{2} \left.\right) \textrm{ } \left(ln\right)^{2} \left(\right. \left|\right. x

Engineering

Mathematics

domain of function

Question

Find the sum of integers in domain of function f(x) = $\sqrt{(6 x - 8 - x^{2}) \ln^{2} (| x - 4 |)}$ .

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(6x – 8 – x²) ln² | x – 4 | $\geq$ 0
⇒ 6x – 8 – x² $\geq$ 0, x = 5, x $\neq$ 4
x² – 6x + 8 $\leq$ 0
x $\in$ [2, 4]
$∴$ D_f = [2, 4) $\cup$ {5}