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Version 15.1 von Martin Stern am 2024/10/15 09:43
Zeige letzte Bearbeiter
1 a)
2
3 b)
4
5 c) Gleichsetzen der Funktionsterme von f und g:
6 {{formula}}f(x)=g(x){{/formula}} //
7 {{formula}}\sqrt{-x+1}=-\sqrt{x+5}+3{{/formula}} //
8 {{formula}}-x+1=x+5-2\cdot 3\cdot\sqrt{x+5}+9{{/formula}} //
9 {{formula}}-2x-13=-6\sqrt{x+5}{{/formula}} //
10 {{formula}}(-2x-13)^2=36(x+5){{/formula}} //
11 {{formula}}4x^2+52x+169=36x+180{{/formula}} //
12 {{formula}}4x^2+16x-11=0{{/formula}} //
13 {{formula}}x_{1,2}=\frac{-16\pm\sqrt{16^2-4\cdot4\cdot(-11)}}{8}{{/formula}} //
14 {{formula}}x_{1,2}=\frac{-16\pm\sqrt{432}}{8}{{/formula}} //
15 {{formula}}x_{1,2}=-2\pm\frac{3}{2}\sqrt{3}{{/formula}} //
16
17 {{formula}}f(x_1)=g(x_1)\approx 0,634{{/formula}} //
18 {{formula}}f(x_2)=g(x_2)\approx 2,366{{/formula}} //
19
20 Die beiden Funktionsgraphen {{formula}}K_f{{/formula}} und {{formula}}K_g{{/formula}} schneiden sich in {{formula}}S_1(-2+\frac{3}{2}\sqrt{3}|0,634){{/formula}} und {{formula}}S_2(-2-\frac{3}{2}\sqrt{3}|2,366){{/formula}}.