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Tentukan nilai dari : 8. ∣ x + 2 ∣ + ∣ 3 x − 1 ∣ + ∣ x ∣ jika x > 2

Tentukan nilai dari :

8. jika

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H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

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Pembahasan

Ingat definisi mutlak berikut: Berdasarkan definisi tersebut, maka Jadi, untuk ,

Ingat definisi mutlak berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar f left parenthesis x right parenthesis close vertical bar end cell equals cell open curly brackets table attributes columnalign left end attributes row cell f left parenthesis x right parenthesis space untuk space f left parenthesis x right parenthesis greater or equal than 0 end cell row cell negative f left parenthesis x right parenthesis space untuk space f left parenthesis x right parenthesis less than 0 end cell end table close end cell end table

Berdasarkan definisi tersebut, maka

  • open vertical bar x plus 2 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell x plus 2 space untuk space x plus 2 greater or equal than 0 space space space space space space space space space space space space space space space space space space space space space space space space x greater or equal than negative 2 end cell row cell negative left parenthesis x plus 2 right parenthesis space untuk space x plus 2 less than 0 minus x minus 2 space space space space space space space space space space space space space space space space space space x less than negative 2 end cell end table close
  • open vertical bar 3 x minus 1 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell 3 x minus 1 space untuk space 3 x minus 1 greater or equal than 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space x greater or equal than 1 third end cell row cell negative left parenthesis 3 x minus 1 right parenthesis space untuk space 3 x minus 1 less than 0 minus 3 x plus 1 space space space space space space space space space space space space space space space space space space space space x less than 1 third end cell end table close
  • open vertical bar x close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell x space untuk space x greater or equal than 0 end cell row cell negative x space untuk space x less than 0 end cell end table close

Jadi, untuk x greater than 2,

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x plus 2 close vertical bar plus open vertical bar 3 x minus 1 close vertical bar plus open vertical bar x close vertical bar end cell equals cell left parenthesis x plus 2 right parenthesis plus left parenthesis 3 x minus 1 right parenthesis plus x end cell row blank equals cell x plus 3 x plus x plus 2 minus 1 end cell row blank equals cell 5 x plus 1 end cell end table

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