Pertanyaan

Diketahui fungsi f ( x ) = sin − 1 ( 1 − x 2 ) , jika f ( n ) = − 2 , maka nilai n adalah...

Diketahui fungsi $f (x) = sin^{- 1} (1 - x^{2})$ , jika $f (n) = - 2$ , maka nilai $n$ adalah...

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Cari turunan , Di dapatkan , diketahui Subtitusi nilai ke Jadi, nilai yang memenuhi adalah . Oleh karena itu, jawaban yang benar adalah C.

Cari turunan f left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent open parentheses 1 minus x squared close parentheses ,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses arcsin open parentheses 1 minus x squared close parentheses close parentheses end cell equals cell equals fraction numerator d over denominator d u end fraction open parentheses arcsin open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses 1 minus x squared close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus u squared end root end fraction fraction numerator d over denominator d x end fraction open parentheses 1 minus x squared close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus open parentheses 1 minus x squared close parentheses squared end root end fraction fraction numerator d over denominator d x end fraction open parentheses 1 minus x squared close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus open parentheses 1 minus x squared close parentheses squared end root end fraction fraction numerator d over denominator d x end fraction open parentheses 1 close parentheses minus fraction numerator d over denominator d x end fraction open parentheses x squared close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus open parentheses 1 minus x squared close parentheses squared end root end fraction open parentheses 0 minus 2 x close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus open parentheses 1 minus x squared close parentheses squared end root end fraction open parentheses negative 2 x close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of x squared end root square root of negative x squared plus 2 end root end fraction open parentheses negative 2 x close parentheses end cell row blank equals cell fraction numerator 1 over denominator x square root of negative x squared plus 2 end root end fraction open parentheses negative 2 x close parentheses end cell row blank equals cell negative 2 times fraction numerator 1 over denominator x square root of negative x squared plus 2 end root end fraction x end cell row blank equals cell negative fraction numerator 1 times thin space 2 x over denominator x square root of negative x squared plus 2 end root end fraction end cell row blank equals cell negative fraction numerator 1 times thin space 2 over denominator square root of negative x squared plus 2 end root end fraction end cell row blank equals cell negative fraction numerator 1 times thin space 2 over denominator square root of negative x squared plus 2 end root end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of negative x squared plus 2 end root end fraction end cell end table$

Di dapatkan $f apostrophe left parenthesis x right parenthesis equals negative fraction numerator 2 over denominator square root of negative x squared plus 2 end root end fraction$ , diketahui

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis n right parenthesis end cell equals cell negative fraction numerator 2 over denominator square root of negative n squared plus 2 end root end fraction rightwards arrow kedua space sisi space dikali space square root of negative n squared plus 2 end root end cell row cell negative fraction numerator 2 over denominator square root of negative n squared plus 2 end root end fraction square root of negative n squared plus 2 end root end cell equals cell negative 2 square root of negative n squared plus 2 end root end cell row 2 equals cell negative 2 square root of negative n squared plus 2 end root end cell row cell 2 square root of negative n squared plus 2 end root end cell equals cell negative 2 rightwards arrow bagi space kedua space ruas space dengan space minus 2 end cell row cell fraction numerator negative 2 square root of negative n squared plus 2 end root over denominator negative 2 end fraction end cell equals cell fraction numerator negative 2 over denominator negative 2 end fraction end cell row cell square root of negative n squared plus 2 end root end cell equals cell 1 rightwards arrow pangkatkan space kedua space ruas end cell row cell open parentheses square root of negative straight n squared plus 2 end root close parentheses squared end cell equals cell 1 squared end cell row cell open parentheses open parentheses negative n squared plus 2 close parentheses to the power of 1 half end exponent close parentheses squared end cell equals cell 1 squared end cell row cell negative n squared plus 2 end cell equals 1 row cell negative n squared end cell equals cell 1 minus 2 end cell row cell negative n squared end cell equals cell negative 1 end cell row cell n squared end cell equals 1 row n equals cell plus-or-minus square root of 1 end cell row n equals 1 row blank blank cell atau space end cell row n equals cell negative 1 end cell end table end style$

Subtitusi nilai ke $f apostrophe left parenthesis x right parenthesis equals negative fraction numerator 2 over denominator square root of negative x squared plus 2 end root end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis 1 right parenthesis end cell equals cell negative fraction numerator 2 over denominator square root of negative 1 squared plus 2 end root end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of 2 minus 1 squared end root end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of 2 minus 1 end root end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of 1 end fraction end cell row blank equals cell negative 2 over 1 end cell row blank equals cell negative 2 end cell row blank blank blank row cell f apostrophe left parenthesis negative 1 right parenthesis end cell equals cell negative fraction numerator 2 over denominator square root of negative left parenthesis negative 1 squared right parenthesis plus 2 end root end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of negative left parenthesis negative 1 right parenthesis plus 2 end root end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of 1 plus 2 end root end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction end cell end table$

Jadi, nilai yang memenuhi adalah n equals 1 .

Oleh karena itu, jawaban yang benar adalah C.