vault backup: 2022-02-23 09:05:32

notes/.obsidian/graph.json

@@ -95,6 +95,6 @@
   "repelStrength": 10.2352941176471,
   "linkStrength": 0.458823529411765,
   "linkDistance": 240,
-  "scale": 0.3138188640425465,
+  "scale": 0.22383929542959702,
   "close": true
 }

notes/.obsidian/plugins/obsidian-activity-history/data.json

@@ -12,8 +12,8 @@
   "checkpointList": [
     {
       "path": "/",
-      "date": "2022-02-21",
-      "size": 780658
+      "date": "2022-02-23",
+      "size": 780770
     }
   ],
   "activityHistory": [
@@ -54,7 +54,15 @@
         },
         {
           "date": "2022-02-21",
-          "value": 1528
+          "value": 1572
+        },
+        {
+          "date": "2022-02-22",
+          "value": 0
+        },
+        {
+          "date": "2022-02-23",
+          "value": 170
         }
       ]
     }

notes/mat/Absolutní hodnota.md

@@ -39,3 +39,7 @@ $-x=66$
 $x=66$ ❌ $[66\not\in x<3]$
 
 $x \geq 3$
+---
+$$\textcolor{red}{|x+1|}+\textcolor{green}{|x-1|}=4$$
+$\textcolor{red}{nulový \space bod \dots -1}$          $\textcolor{green}{nulový \space bod \dots 1}$
+

notes/mat/Funkce/Příklady.md

@@ -0,0 +1,312 @@
+---
+Date: 2022-03-02
+---
+# Příklady
+
+## Určete definiční obory funkcí
+---
+$f_1: y = x^3 - x^2 + 1$
+$D_{f_1} = \mathbb{R}$
+
+---
+$f_2:y=\frac1{6-4x}$
+$D_{f_2} = \mathbb{R} - \{1.5\}$
+
+---
+$f_3:y=\frac1{4x^2-9}$
+$D_{f_3} = \mathbb{R} - \{1.5\}$
+
+---
+$f_4: y = \frac{\sqrt{4-2x}}3$
+$D_{f_4} = (-\infty; 2\rangle$
+
+---
+$f_5:y=\sqrt{x-2}+\frac1x$
+$D_{f_5}=\langle2;\infty) - \{0\}$
+
+---
+$f_6:y=\frac{\sqrt{x+3}}{\sqrt{x+7}}$
+$D_{f_6} = \langle-3;\infty) - \{-7\}$
+
+---
+$f_7:y=\sqrt\frac{x+3}{x+7}$
+$D_{f_7} = \langle-3;\infty)$
+
+---
+## Rozhodněte, zda číslo $d$ náleží $H(f_i)$
+---
+$d=7$
+$f_1:y=3x-4$
+$f_1^{-1}: x=\frac{y+4}3$
+$D_{f_1^{-1}}=\mathbb{R}$
+$H_{f_1}=\mathbb{R}$
+$7\in\mathbb{R}$
+✔️
+
+---
+$d=5$
+$f_2:y=-5$
+$H_{f_2} = \{-5\}$
+$5 \not\in \{-5\}$
+❌
+
+---
+$d=0$
+$f_3:y=\frac1{x+3}$
+$f_3^{-1} : x=\frac1y-3$
+$D_{f_3^{-1}} = \mathbb{R} - \{0\}$
+$0\not\in\mathbb{R}-\{0\}$
+❌
+
+---
+$d=-4$
+$f_4:y=\frac{x+1}{x-2}$
+$f_4^{-1}:2=\frac1y$
+$y = \frac{x+1}{x-2}$
+$y(x-2)=x+1$
+$y(x-2)-x=1$
+$x-2=\frac{(1+x)}y$
+
+
+---
+$d=\frac12$
+$f_5:y=\frac1{x^2-1}$
+$f_5^{-1}: x=\sqrt{\frac1y+1}$
+$D_{f_5^{-1}} = H_{F_5} = (-1;\infty)$
+$\frac12 \in (-1; \infty)$
+✔️
+
+---
+
+## Určete číslo $b\in\mathbb{R}$ za předpokladu, že:
+
+---
+graf funkce $f:y=6x+b$, prochází bodem $A[0;4]$
+$f(0) = 4$
+$6*0 + b = 4$
+$b = 4$
+
+---
+graf funkce $f:y=\frac32x+b$, prochází bodem $A[-2;9]$
+$f(-2) = 9$
+$\frac32*(-2)+b=9$
+$-3+b=9$
+$b=12$
+
+---
+
+## Určete číslo $a\in\mathbb{R}$ za předpokladu, že:
+
+---
+graf funkce $f:y=ax+2$, prochází bodem $A[-2;6]$
+$f(-2) = 6$
+$-2a+2=6$
+$-2a=4$
+$-a=2$
+$a=-2$
+
+---
+graf funkce $f:y=ax-2$, prochází bodem $A[1;2]$
+$f(1)=2$
+$1a-2=2$
+$a=4$
+
+
+---
+$$
+-5-2x=4x+7
+$$
+$$
+x=-2
+$$
+---
+$$
+8000+100x=10000+80x
+$$
+$$
+x=100
+$$
+
+
+---
+$$x + \frac2x - 1 = \frac{x + 6}{x + 2}$$
+$$x(x+2) + 4 - (x+2) = x + 6 \space | *(x+2)$$
+$[x\neq-2]$
+$$x^2+2x+4-x-2=x+6$$
+$$x^2+x+2=x+6$$
+$$x^2+x-4=x$$
+$$x^2-4=0$$
+$$2 = x$$
+
+	
+---
+
+$$\frac{x+2}{x-1}=\frac{x+6}{x+2} \space | *(x-1)(x+2)$$
+$[x\neq1]; [x\neq-2]$
+$$(x+2)^2 = (x+6)(x-1)$$
+$$x^2+4x+4=x^2+5x-6$$
+$$4x+4=5x-6$$
+$$x=10$$
+
+---
+
+$$\frac{2x+1}{x-3}=\frac{4x+2}{2x-1} \space | *(x-3)(2x-1)$$
+$[x\neq3]; [x\neq\frac12]$
+$$(2x+1)(2x-1)=(4x+2)(x-3)$$
+$$4x^2-1=4x^2-10x-6 \space|-4x^2$$
+$$-1=10x-6 \space |+6$$
+$$5=10x\space|:10$$
+$$x=0.5$$
+$$K=\{-\frac12\}$$
+
+---
+
+$$\frac{x+3}{x-2}=4+\frac5{x-2} \space | *(x-2)$$
+$[x\neq2]$
+$$x+3=4(x-2)+5$$
+$$x+3=4x-3 \space |-x$$
+$$3=3x-3 \space |+3$$
+$$6=3x \space | :3$$
+$$x=2$$
+$$K=\{\emptyset\}$$
+```ad-sentence
+Výsledné x nemá řešení, protože podmínka zakáže výslednou hodnotu (x nesmí být 2, ale x vyšlo 2)
+```
+
+---
+
+$$\frac{x+4}{x+5}=2-\frac1{x+5} \space | *(x+5)$$
+$[x\neq-5]$
+$$x+4=2(x+5)-1$$
+$$x+4=2x+9 \space | -x$$
+$$4=x+9 \space | -9$$
+$$x=-5$$
+$$K=\{\emptyset\}$$
+
+---
+
+$$\frac{x-2}{x+3}=2-\frac5{x+3} \space | * (x+3)$$
+$[x\neq-3]$
+$$x-2=2(x+3)-5$$
+$$x-2=2x+1 | -x-1$$
+$$x=-3$$
+$$K=\{\emptyset\}$$
+---
+
+$$\frac{x+8}{x+3}=1+\frac5{x+3} \space | *(x+3)$$
+$[x\neq-3]$
+$$x+8=1(x+3)+5$$
+$$x+8=x+8 \space | -8$$
+$$0x=0$$
+$$K=\{\mathbb{R} - \{-3\}\}$$
+
+---
+
+$$\frac{x+2}{x+5} = 1-\frac3{x+5} \space | * (x+5)$$
+$[x\neq-5]$
+$$x+2=x+2 \space | -2-x$$
+$$0x=0$$
+$$K=\{\mathbb{R}-\{-5\}\}$$
+
+---
+
+$$\frac{x-3}{x+2}=1-\frac6{x+2} \space | *(x+2)$$
+$[x\neq-2]$
+$$x-3=x-4 \space | -x+4$$
+$$1=0x$$
+$$K=\{\emptyset\}$$
+
+---
+
+$$\frac{2x-4}{x-2}=1-\frac2{x-2} \space | *(x-2)$$
+$[x\neq2]$
+$$2x-4=x-4 | +4$$
+$$2x=x \space |-x$$
+$$x=0$$
+$$K={0}$$
+
+---
+
+$$\frac{x+3}5 = x$$
+$$\frac{x+3}5-x=0$$
+$$x+3-5x=0$$
+$$-4x+3=0$$
+$$4x=3$$
+$$x=\frac34$$
+---
+$$7(1-x)-4(x-8)=(2-x)11$$
+$$7-7x-4x+32=22-11x$$
+$$-11x+39=22-11x$$
+$$39\neq22$$
+
+---
+
+$$\frac{3+2x}2-\frac76=5x-\frac{12x-1}3$$
+$$9+6x-7=30x-24x+2$$
+$$6x+2=6x+2$$
+$$2=2$$
+---
+
+$$x-6=\frac{7x-3}3-\frac{3(x+2)}4$$
+$$12x-72=28x-12-9x-18$$
+$$12x-72=27x-30$$
+$$-72=7x-30$$
+$$-42=4x$$
+$$x=-6$$
+---
+$$a(a-1)+3=(a+2)(a-2)$$
+$$aa-a+3=aa-4$$
+$$-a+3=-4$$
+$$a=7$$
+---
+$$x-(3x-(4x-(3x-1)-1)+3)=-5$$
+$$x-3x-3+4x-1-3x+1=-5$$
+$$-x-3=-5$$
+$$x=2$$
+---
+$$x-3(x-5(x-4))=10(x-3)$$
+$$x-3x+15x-60=10x-30$$
+$$13x-60=10x-30$$
+$$3x-60=-30$$
+$$x=10$$
+---
+$$3-\frac32(\frac{5x}6-2)=(1\frac12)x-\frac12(\frac12x-9.5)$$
+$$3-\frac{15*6x}{2}+\frac62=1.5x-\frac{x}4+\frac{9.5}2$$
+$$12-30*6x+12=6x-x+19$$
+$$\frac1{37}=x$$
+🤷
+
+---
+$$\frac6{x-5}+1=\frac{2x-4}{x-5}$$
+$$6+x-5=2x-4$$
+$$x=5$$
+nemůže být
+
+---
+$$\frac{2x+5}{x+2}+\frac1{2+x}=3$$
+$$2x+5+1=3x+6$$
+$$2x+6=3x+6$$
+$$x=0$$
+---
+$$\frac{2x+4}{3x-1}=\frac25-\frac{x+5}{1-3x}$$
+$$\frac{2x+4}{3x-1}=\frac25+\frac{x+5}{3x-1}$$
+$$2x+4=\frac{2(3x-1)}5 +x+5$$
+$$x=\frac{6x-2}5+1$$
+$$x=-3$$
+---
+$$\frac{x+7}{x-5}+\frac{x+5}{x-7}=2$$
+$$(x+7)(x-7)+(x+5)(x-5)=2(x-5)(x-7)$$
+$$x^2-7^2+x^2-5^2=2(x^2-7x-5x+35)$$
+$$2x^2-7^2-5^2=2x^2-14x-10x+70$$
+$$2x^2-49-25=2x^2-24x+70$$
+$$2x^2-74=2x^2-24x+70$$
+
+$$24x=144$$
+$$x=6$$
+---
+$$\frac{17}{x+1}-\frac5{x^2+x}=\frac6x$$
+$$\frac{17}{x+1}-\frac5{x(x+1)}=\frac6x \space | :x(x+1)$$
+$$17x-5=6(x+1)$$
+$$17x-5=6x+6 |+5$$
+$$11x=11$$
+$$x=1$$