**Determine the domain of each of the following functions: 1. f(x) = x + 10 6. A(x) = x2 -2 2. F(x) = 2 3 π₯ + 5 7. H(x) = βπ₯ β 2 3. g(x) = 5 β 3x 8. K(x) = βπ₯ 2 β 2 4. g(x) = 1 (π₯+5)(π₯β1) 9. C(x) = 2x3 + 4x2 - 2x + 1 5. b(x) = π₯β1 π₯ 2+5π₯+6 10. βπ₯+1 π₯β2**

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The domain of the function(D) is the set of all values that argument might take. I will assume that x is a real number. Also the conditions is inaccurate, so i don't fully sure whether i recognized it correctly in each case, but it must be close to it

f(x) = x + 10.Β $D:x\isin R$

$A(x) = x^2 -2$Β .Β $D:x\isin R$

$F(x) = 2^{3π₯} + 5$Β .Β $D:x\isin R$

$H(x) = \sqrtπ₯ β 2$Β . The value under the square root must be non-negative, soΒ $D:x\isin [0,+\infty)$

g(x) = 5 β 3x .Β $D:x\isin R$

$K(x) = \sqrt{x^2 β 2}$Β .Β $D:x^2-2β₯0\implies x^2β₯2\implies D:x\isin (-\infty,-\sqrt2)\cup(\sqrt2,+\infty)$

$g(x) = {\frac 1 {(π₯+5)(π₯β1)}}$Β . Cannot divide by 0, soΒ $D:(x+5)(x-1)\not=0\implies D:x\in R$Β \ {-5, 1}

$C(x) = 2x^3 + 4x^2 - 2x + 1$Β .Β $D:x\isin R$

$b(x) = π₯β{\frac 1 {x^2+5x+6}}$Β .Β $D:x^2+5x+6\not=0\implies D:x\in R$Β \ {-3, -2}

$f(x)={\frac {\sqrt{x-1}} {x-2}}$Β .Β $D:(x-1β₯0)\land (x-2\not=0)\implies D:x\isin [1,+\infty)$Β \ {2}