Question

Determine the domain of each of the following functions: 1. f(x) = x + 10 6. A(x) = x2 -2 2. F(x) = 2 3 𝑥 + 5 7. H(x) = √𝑥 − 2 3. g(x) = 5 – 3x 8. K(x) = √𝑥 2 − 2 4. g(x) = 1 (𝑥+5)(𝑥−1) 9. C(x) = 2x3 + 4x2 - 2x + 1 5. b(x) = 𝑥−1 𝑥 2+5𝑥+6 10. √𝑥+1 𝑥−2 

Answer 1

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. $D:x\isin R$

$A(x) = x^2 -2$ . $D:x\isin R$

$F(x) = 2^{3𝑥} + 5$ . $D:x\isin R$

$H(x) = \sqrt𝑥 − 2$ . The value under the square root must be non-negative, so $D:x\isin [0,+\infty)$

g(x) = 5 – 3x . $D:x\isin R$

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

$g(x) = {\frac 1 {(𝑥+5)(𝑥−1)}}$ . Cannot divide by 0, so $D:(x+5)(x-1)\not=0\implies D:x\in R$ \ {-5, 1}

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

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

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