Definiční obor výrazu
Urči v \mathbb{R} definiční obor výrazu:
\large \Large \frac{{2x}}{{x^{3}+6x^{2}+9x}}\large
Podmínka:
I.\ x^{3} + 6x^{2} + 9x \ne 0 \to x\cdot\left( {x^{2} + 6x + 9} \right) \ne 0 \to x\cdot{\left( {x + 3} \right)^2} \ne 0 \to x_{1} \ne\ – 3,\ x_{2} \ne 0
\large D\left( x\right) = \mathbb{R}- \left \{ { - 3;1} \right \}
Podmínka:
I.\ x^{3} + 6x^{2} + 9x \ne 0 \to x\cdot\left( {x^{2} + 6x + 9} \right) \ne 0 \to x\cdot{\left( {x + 3} \right)^2} \ne 0 \to x_{1} \ne\ – 3,\ x_{2} \ne 0
\large D\left( x\right) = \mathbb{R}- \left \{ { - 2;0} \right \}
Podmínka:
I.\ x^{3} + 6x^{2} + 9x \ne 0 \to x\cdot\left( {x^{2} + 6x + 9} \right) \ne 0 \to x\cdot{\left( {x + 3} \right)^2} \ne 0 \to x_{1} \ne\ – 3,\ x_{2} \ne 0
\large D\left( x\right) = \mathbb{R}- \left \{ { - 3;2} \right \}
Podmínka:
I.\ x^{3} + 6x^{2} + 9x \ne 0 \to x\cdot\left( {x^{2} + 6x + 9} \right) \ne 0 \to x\cdot{\left( {x + 3} \right)^2} \ne 0 \to x_{1} \ne\ – 3,\ x_{2} \ne 0
\large D\left( x\right) = \mathbb{R}- \left \{ { - 3;0} \right \}