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Pertanyaan

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Fungsi y equals f left parenthesis x right parenthesis di atas mempunyai persamaan ....

  1. f open parentheses x close parentheses equals 2 to the power of negative x plus 1 end exponent 

  2. f open parentheses x close parentheses equals 2 to the power of x plus 1 

  3. f open parentheses x close parentheses equals 2 to the power of x plus 2 

  4. f open parentheses x close parentheses equals 2 to the power of negative x minus 2 end exponent 

  5. f open parentheses x close parentheses equals 2 to the power of negative x end exponent plus 2 

Pembahasan Soal:

Grafik tersebut, melalui 3 titik yaitu open parentheses 0 comma space 3 close parentheses comma space open parentheses negative 1 comma space 4 close parentheses dan open parentheses negative 2 comma space 6 close parentheses, sehingga permisalan fungsi eksponen yang kita gunakan adalah begin mathsize 14px style f open parentheses x close parentheses equals b times a to the power of x plus c end style. Subtitusikan ketiga titik tersebut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell b times a to the power of x plus c end cell row cell open parentheses 0 comma space 3 close parentheses end cell rightwards arrow cell 3 equals b times a to the power of 0 plus c end cell row 3 equals cell b times 1 plus c end cell row 3 equals cell b plus c space space space space space... open parentheses straight i close parentheses end cell end table  

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell b times a to the power of x plus c end cell row cell open parentheses negative 1 comma space 4 close parentheses end cell rightwards arrow cell 4 equals b times a to the power of negative 1 end exponent plus c end cell row 4 equals cell b over a plus c space space space space space... open parentheses ii close parentheses end cell end table   

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell b times a to the power of x plus c end cell row cell open parentheses negative 2 comma space 6 close parentheses end cell rightwards arrow cell 6 equals b times a to the power of negative 2 end exponent plus c end cell row 6 equals cell b times a to the power of negative 2 end exponent plus c end cell row 6 equals cell b over a squared plus c space space space space space... open parentheses iii close parentheses end cell end table  

Eliminasi persamaan begin mathsize 14px style left parenthesis straight i right parenthesis end style dan begin mathsize 14px style open parentheses ii close parentheses end style.

table row cell b over a plus c equals 4 end cell row cell b plus c equals 3 end cell row cell b over a minus b equals 1 space space end cell end table minus space... open parentheses iv close parentheses   

Eliminasi persamaan begin mathsize 14px style open parentheses ii close parentheses end style dan begin mathsize 14px style open parentheses iii close parentheses end style.

table row cell b over a squared plus c equals 6 end cell row cell b over a plus c equals 4 end cell row cell b over a squared minus b over a equals 2 end cell row cell 1 over a open parentheses b over a minus b close parentheses equals 2 end cell end table minus space... open parentheses straight v close parentheses  

Dari persamaan begin mathsize 14px style open parentheses iv close parentheses end stylebegin mathsize 14px style open parentheses straight v close parentheses end style dan begin mathsize 14px style open parentheses straight i close parentheses end style diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over a open parentheses b over a minus b close parentheses end cell equals 2 row cell 1 over a times 1 end cell equals 2 row cell 1 over a end cell equals 2 row 1 equals cell 2 a end cell row a equals cell 1 half end cell end table       

table attributes columnalign right center left columnspacing 0px end attributes row cell b over a minus b end cell equals 1 row cell fraction numerator b over denominator begin display style 1 half end style end fraction minus b end cell equals 1 row cell 2 b minus b end cell equals 1 row b equals 1 end table   

      table attributes columnalign right center left columnspacing 0px end attributes row cell b plus c end cell equals 3 row cell 1 plus c end cell equals 3 row c equals 2 end table      

Sehingga fungsinya:

 table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell b times a to the power of x plus c end cell row blank equals cell 1 times open parentheses 1 half close parentheses to the power of x plus 2 end cell row blank equals cell open parentheses 1 half close parentheses to the power of x plus 2 end cell row blank equals cell 2 to the power of negative x end exponent plus 2 end cell end table   

Fungsi eksponen dari grafik tersebut adalah f open parentheses x close parentheses equals 2 to the power of negative x end exponent plus 2.

Jadi, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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