Analisi matematica 1- Domini

1) \( g(x) = \frac{9-5x^2}{x^2+x-2} \)

\((x+2)(x-1) \neq 0\)

\(x \neq -2\), \(x \neq 1\)

11) \( g(x) = \ln(x^2) \)

\(x^2 > 0\)

\(x \neq 0\)

\(x \neq 0\)

10) \( g(x) = \ln\left(\frac{x-4}{2x+6}\right) \)

\(\frac{x-4}{2x+6} > 0\)

\(x>0\)

\(x \neq -3\)

\(\{ x0 \} \leftarrow \text{is.} \)

\(x \neq -3\)

12) \( x^3 e^{-x^3} \)

20) \(\sqrt{\frac{x+1}{2x-8}}\)

\(\frac{x+1}{2x-8} \geq 0\)

\(x \geq -1\)

\(x \(x \leq -1 \vee x > 4\)

13) \(\frac{\sqrt{1+x-1}}{\sqrt{1+t}} \)

\(x \geq 0\)

\(\sqrt{1+2x}\)

\(\{ 2x \geq -1 \}\(x \geq -\frac{1}{2}\(-\frac{2}{3}

16) \(g(x) = \ln \left(\frac{x-4}{2x+6}\right)\)

 { \(\frac{x-4}{2x+6} > 0\) \(2x+6 ≠ 0\) }  \(\frac{x-4}{2x+6} > 0\)   \(x > 0\)   \(x > -3\) \(x < -3\) V \(x > 0\)   { \(x < -3\) V \(x > 0\)   \(x ≠ -3\)

24) \(x^3 * e^{-x^3}\)

29) \(\sqrt{\frac{x+1}{2x-8}}\)

  { \(\frac{x+1}{2x-8} ≥ 0\) \(2x-8 ≠ 0\) }   { \(x ≥ -1\) \(x ≠ 4\) }\(x ≤ -1\) V \(x > 4\)

19) \(\sqrt{\frac{1+x-1}{1 ± 2x}}\)

\(x < 0\)   \(\sqrt{1 ± 2x}\){ \(2x ≥ -1\) }   { \(x ≥ -1/2\) \(-1/2 < x < 0\) unione D = [-1/2,1 + ∞)

13) \(\radic;|x|(x²-1)\)

\(x ≥ 0\)\(\radic;x(x² - 1)\)         \(x(x² - 1) ≥ 0\)

\(x ≥ 0\)

\(x ≤ -1\) ∨ \(x ≥ 1\)

\(x ≥ 1\)    [1, +∞)

\(x < 0\)\(\radic;-x(x² - 1)\)     -x\((x² - 1) ≥ 0\)

\(x < 0\)

\(x ≤ -1\) ∨ \(x ≥ 1\)

\(x ≤ -1\)    (-∞, -1]

Dom: (-∞, -1] ∪ [1, +∞)

21) \(\radic;x+1 + \radic;x-1\)

\(x ≥ -1\)

\(x ≥ 1\)

[1, +∞)

22) \(\radic;x - \radic;³x / x² - 3x\)

\(x ≥ 0\)

\(3 - x ≥ 0\)

\((x - 3) ≠ 0\)

\(x ≥ 0\)

\(x ≤ 3\)

\(x ≠ 0\)

\(x ≠ 3\)

\(0 < x < 3\)

27) \(y = tg 3x = sin 3x / cos 3x\)

      \(cos 3x ≠ 0\)

\(3x ≠ π/2 + kπ\)    \(x ≠ π/6 + kπ/3\)

292) \(\log(2 sen x - 1)\)

\(2 sen x > 0\) \(sen x > 1/2\)

\(π/6 < x < 5π/6\)

29) \(\radic;x-2 -1 / log(\radic;x-1)\)

\(x-2 ≥ 0\) \(log(\radic;x-1) ≠ 0\) \(\radic;x-1 > 0\) \(x ≥ 0\) \(x ≥ 2\) \(x ≥ 0\) \(x > 1\) \(\radic;x-1 ≠ 1\)

\(x ≥ 2\) Λ \(x ≠ 4\)

[2, 4) ∪ (4, +∞)

30) \(arcsin(x/x+1)\)

\(-1 ≤ x/x+1 ≤ 1\) \(x+1 > 0\) \(x/x+1 ≤ 0\) \(x+1 > 0\) \(x-1 / x+1 ≤ 0\) \(2x+1 ≥ 0\) \(x ≥ -1/2\) \(x > -1\)

\(x ≥ -1/2\)

[-1/2, +∞)

1) ³\(\radic;(ln|sinx|)\)

\(sinx > 0\)

\(ln|sinx| ≥ 0\)

\(sinx > 0\)

\(sinx ≥ 1\)

\(0 < x < π → 0 < x < π\)

_{x =}\(x = π\)

\(sin² x + cos² x\)

\(3 sinx - &sq; 3 sinx\)

\(3 sinx ≠ &sqrt;3 sin x\)

\(tg x ≠ &frac13;\radic;3\)

\(x ≠ π/6 + kπ\)

\(x ≠ π/3\)

\(\radic;^4-x2 - ln(x²-4x-5)\)

\(4-x²/2x ≥ 0\)

\(2x ≠ 0\)

\(x²-4x-5 > 0\)

\((x-5)(x+1) > 0\)   \(x > 5\)   \(x > -1\)

\(x -1 < x < 5\)

\(-2 &mid; -1 &mid; 0 &mid; 2 &mid; 5\)

\(-2 < x < 0\) ∨ \(x ≥ 2\)

\(-2 < x < 1\) ∨ \(x > 5\)