Fungsi f:R→R dinyatakan dengan f(x)=2x+1x−3, x=−21. Jika f−1 invers fungsi f, nilaif−1(4) adalah ....

Pertanyaan

Fungsi $f:R\rightarrow R$ dinyatakan dengan $f open parentheses x close parentheses equals fraction numerator x minus 3 over denominator 2 x plus 1 end fraction comma space x not equal to negative 1 half$ . Jika $f^{-1}$ invers fungsi f, nilai $f^{-1}\left(4\right)$ adalah ....

-4
-2
-1
1
2

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Ingat kembali cara cepat invers fungsi berikut :

$f open parentheses x close parentheses equals fraction numerator a x plus b over denominator c x plus d end fraction rightwards double arrow f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative d x plus b over denominator c x minus a end fraction$

Maka,

$f open parentheses x close parentheses equals fraction numerator x minus 3 over denominator 2 x plus 1 end fraction rightwards double arrow f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative x minus 3 over denominator 2 x minus 1 end fraction$

Saat maka invers fungsi menjadi :

$f to the power of negative 1 end exponent open parentheses 4 close parentheses equals fraction numerator negative 4 minus 3 over denominator 2 open parentheses 4 close parentheses minus 1 end fraction equals fraction numerator negative 7 over denominator 7 end fraction equals negative 1$