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Gegee: $f(x) = an x$ en $g(x) = ext{cos}(x - 45^ ext{o})$ vir $x ext{ } e [0^ ext{o}; 360^ ext{o}]$ 5.1 Teken sketsgrafieke van $f$ en $g$ op dieselfde asstelstel op die rooster wat in die ANTWOORDEBOOK verskaf is - NSC Technical Mathematics - Question 5 - 2021 - Paper 1

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Gegee:---$f(x)-=--an-x$-en-$g(x)-=--ext{cos}(x---45^-ext{o})$-vir-$x--ext{-}--e-[0^-ext{o};-360^-ext{o}]$----5.1---Teken-sketsgrafieke-van-$f$-en-$g$-op-dieselfde-asstelstel-op-die-rooster-wat-in-die-ANTWOORDEBOOK-verskaf-is-NSC Technical Mathematics-Question 5-2021-Paper 1.png

Gegee: $f(x) = an x$ en $g(x) = ext{cos}(x - 45^ ext{o})$ vir $x ext{ } e [0^ ext{o}; 360^ ext{o}]$ 5.1 Teken sketsgrafieke van $f$ en $g$ op dieselfde as... show full transcript

Worked Solution & Example Answer:Gegee: $f(x) = an x$ en $g(x) = ext{cos}(x - 45^ ext{o})$ vir $x ext{ } e [0^ ext{o}; 360^ ext{o}]$ 5.1 Teken sketsgrafieke van $f$ en $g$ op dieselfde asstelstel op die rooster wat in die ANTWOORDEBOOK verskaf is - NSC Technical Mathematics - Question 5 - 2021 - Paper 1

Step 1

5.2.1 $f$ ongedeffinieer is

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Answer

Die funksie f(x)=anxf(x) = an x is ongedeffinieer waar die noemer van die tangensfunksie nul is, wat voorkom by:\

x=90exto+kimes180exto extwaarkextngeheelgetalisx = 90^ ext{o} + k imes 180^ ext{o} \ ext{ waar } k ext{ 'n geheel getal is}\

In die gegewe interval [0exto;360exto][0^ ext{o}; 360^ ext{o}] is die waardes x=90extox = 90^ ext{o} en x=270extox = 270^ ext{o}.

Step 2

5.2.2 $f(x) imes g(x) ext{ } 0$ waar $x ext{ } e [90^ ext{o}; 180^ ext{o}]$

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Answer

Die produk f(x)imesg(x)f(x) imes g(x) is groter as nul wanneer albei funksies positief of albei funksies negatief is.\

  1. xexte[0exto;90exto]x ext{ } e [0^ ext{o}; 90^ ext{o}] (wat nie in die interval is)\
  2. xexte[90exto;135exto]x ext{ } e [90^ ext{o}; 135^ ext{o}] of x=180extox = 180^ ext{o}\
  3. xx behoort aan die interval [90exto;135exto][90^ ext{o}; 135^ ext{o}] of x=180extox = 180^ ext{o}.

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