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Zuletzt geändert von Henrik Horstmann am 2026/10/19 21:33
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1 (%class="abc"%)
2 1.
3 {{formula}}\begin{aligned}
4 &D_f = \mathbb{R}^* \quad \text{und} \quad W_f = \mathbb{R}^* \\
5 &D_g = \mathbb{R} \quad \text{und} \quad W_g = [4,\infty[ \\
6 &f(g(x)) = \frac{1}{x^2+4} \\
7 &g(x) \neq 0 \iff x^2+4 \neq 0 \iff x^2 \neq -4 \implies x \in \mathbb{R} \\
8 &D_{f \circ g} = \mathbb{R} \quad \text{und} \quad W_{f \circ g} = \left]0,\frac{1}{4}\right]
9 \end{aligned}{{/formula}}
10 1.
11 {{formula}}\begin{aligned}
12 &D_f = \mathbb{R}_+ \quad \text{und} \quad W_f = \mathbb{R}_+ \\
13 &D_g = \mathbb{R} \quad \text{und} \quad W_g = \mathbb{R} \\
14 &f(g(x)) = \sqrt{2x - 6} \\
15 &g(x) \geq 0 \iff 2x - 6 \geq 0 \iff 2x \geq 6 \iff x \geq 3 \\
16 &D_{f \circ g} = [3,\infty[ \quad \text{und} \quad W_{f \circ g} = [0,\infty[
17 \end{aligned}{{/formula}}
18 1.
19 {{formula}}\begin{aligned}
20 &D_f = \mathbb{R} \setminus \{2\} \quad \text{und} \quad W_f = \mathbb{R}^* \\
21 &D_g = \mathbb{R} \quad \text{und} \quad W_g = [-1,\infty[ \\
22 &f(g(x)) = \frac{1}{x^2-3} \\
23 &g(x) = 2 \iff x^2-1 = 2 \iff x^2 = 3 \iff x = \pm\sqrt{3} \\
24 &D_{f \circ g} = \mathbb{R} \setminus \{-\sqrt{3},\sqrt{3}\} \\
25 &\qquad W_{f \circ g} = \left]-\infty,-\frac{1}{3}\right[ \cup \left]0,\infty\right[
26 \end{aligned}{{/formula}}