Perhatikan gambar berikut. Fungsi di atas mempunyai persamaan ....

Pertanyaan

Perhatikan gambar berikut.

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

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

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 $begin mathsize 14px style open parentheses iv close parentheses end style$ , $begin mathsize 14px style open parentheses straight v close parentheses end style$ 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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