Pertanyaan

Diketahui fungsi f ( x ) = x 2 − 2 x − 3 , x ∈ R . Agar f merupakan fungsi bijektif, tentukan: b. rumus fungsi f − 1 ,

Diketahui fungsi $f (x) = x^{2} - 2 x - 3, x \in R$ . Agar $f$ merupakan fungsi bijektif, tentukan:
b. rumus fungsi $f^{- 1}$ ,

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Rumus fungsi invers untuk fungsi kuadrat adalah: Karena sehingga diperoleh: Jadi, rumus adalah:

Rumus fungsi invers untuk fungsi kuadrat adalah:

$begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative b minus square root of b squared minus 4 a open parentheses c minus x close parentheses end root over denominator 2 a end fraction comma space jika space x less or equal than negative fraction numerator b over denominator 2 a end fraction f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative b plus square root of b squared minus 4 a open parentheses c minus x close parentheses end root over denominator 2 a end fraction comma space jika space x greater or equal than negative fraction numerator b over denominator 2 a end fraction end style$

Karena sehingga diperoleh:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative open parentheses negative 2 close parentheses plus-or-minus square root of open parentheses negative 2 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses open parentheses negative 3 close parentheses minus x close parentheses end root over denominator 2 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus square root of 16 plus 4 x end root over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus square root of 16 plus 4 x end root over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus square root of 4 open parentheses 4 plus x close parentheses end root over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus 2 square root of 4 plus x end root over denominator 2 end fraction end cell row blank equals cell 1 plus-or-minus square root of 4 plus x end root end cell end table end style$

Jadi, rumus adalah: