Pertanyaan

2. Fungsi ditentukan oleh . Jika f − 1 ( a ) = − 2 , tentukan nilai a !

2. Fungsi f colon straight real numbers rightwards arrow straight real numbers ditentukan oleh f open parentheses x close parentheses equals 2 over 7 open parentheses x minus 5 close parentheses . Jika $f^{- 1} (a) = - 2$ , tentukan nilai $a!$

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai

Pembahasan

Perhatikan penghitungan berikut! Jadi, nilai

Perhatikan penghitungan berikut!

$f left parenthesis x right parenthesis equals 2 over 7 open parentheses x minus 5 close parentheses Misalkan space y equals f left parenthesis x right parenthesis space maka space x equals f to the power of negative 1 end exponent open parentheses x close parentheses y equals fraction numerator 2 x minus 10 over denominator 7 end fraction 7 y equals 2 x minus 10 7 y plus 10 equals 2 x fraction numerator 7 y plus 10 over denominator 2 end fraction equals x sehingga comma f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 7 x plus 10 over denominator 2 end fraction.$

$f to the power of negative 1 end exponent open parentheses a close parentheses equals fraction numerator 7 a plus 10 over denominator 2 end fraction minus 2 space space space space space equals fraction numerator 7 a plus 10 over denominator 2 end fraction minus 2 open parentheses 2 close parentheses space equals 7 a plus 10 minus 4 space space space space space space equals 7 a plus 10 minus 4 minus 10 equals 7 a minus 14 space space space space space equals 7 a fraction numerator negative 14 over denominator 7 end fraction space space space space equals a minus 2 space space space space space space space equals a$

Jadi, nilai a equals negative 2.