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Pertanyaan

Grafik begin mathsize 14px style y equals 3 to the power of x plus 1 end exponent space minus space open parentheses 1 over 9 close parentheses to the power of x end style berada  di bawah grafik y = 3x + 1 jika ....

  1. 0 < x < 1

  2. x > 1

  3. x < 0

  4. x > 3

  5. 1 < x < 3

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Supaya space grafik space straight y equals 3 to the power of straight x plus 1 end exponent minus open parentheses 1 over 9 close parentheses to the power of straight x space berada space di space bawah space grafik space straight y equals 3 to the power of straight x plus 1 comma space maka  3 to the power of straight x plus 1 end exponent minus open parentheses 1 over 9 close parentheses to the power of straight x less than 3 to the power of straight x plus 1  3 to the power of straight x.3 to the power of 1 minus open parentheses 1 over 3 squared close parentheses to the power of straight x less than 3 to the power of straight x plus 1  3.3 to the power of straight x minus 3 to the power of negative 2 straight x end exponent less than 3 to the power of straight x plus 1  3.3 to the power of straight x minus open parentheses 3 to the power of straight x close parentheses to the power of negative 2 end exponent less than 3 to the power of straight x plus 1    Misalkan space straight a equals 3 to the power of straight x comma space karena space 3 to the power of straight x greater than 0 space maka space straight a greater than 0 comma space sehingga  3 straight a minus straight a to the power of negative 2 end exponent less than straight a plus 1  3 straight a minus 1 over straight a squared less than straight a plus 1  3 straight a cubed minus 1 less than straight a cubed plus straight a squared  2 straight a cubed minus straight a squared minus 1 less than 0  left parenthesis straight a minus 1 right parenthesis left parenthesis 2 straight a squared plus straight a plus 1 right parenthesis less than 0  Perhatikan space bahwa space bentuk space 2 straight a squared plus straight a plus 1 space adalah space definit space positif space karena  memiliki space straight D less than 0 space dan space straight a greater than 0 comma space sehingga space 2 straight a squared plus straight a plus 1 greater than 0  Akibatnya  straight a minus 1 less than 0  straight a less than 1    Karena space straight a greater than 0 comma space maka  0 less than straight a less than 1  box enclose 0 less than 3 to the power of straight x less than 1 end enclose    Untuk space 3 to the power of straight x greater than 0 comma space berlaku space untuk space semua space nilai space straight x space bilangan space real.  Untuk space 3 to the power of straight x less than 1 comma space maka  3 to the power of straight x less than 1  3 to the power of straight x less than 3 to the power of 0  box enclose straight x less than 0 end enclose

 

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