Pertanyaan

Tentukan invers fungsi f ( x − 2 ) = x x − 6 .

Tentukan invers fungsi $f (x - 2) = \frac{x - 6}{x}$ .

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

invers fungsi adalah .

invers fungsi $f left parenthesis x minus 2 right parenthesis equals fraction numerator x minus 6 over denominator x end fraction$ adalah $fraction numerator 2 x plus 4 over denominator 1 minus x end fraction$ .

Pembahasan

Fungsi didapatkan: Invers dari didapatkan: Jadi, invers fungsi adalah .

Fungsi f open parentheses x close parentheses didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x minus 2 end cell row x equals cell y plus 2 rightwards arrow x plus 2 end cell row blank blank blank row cell f open parentheses x close parentheses end cell equals cell fraction numerator open parentheses x plus 2 close parentheses minus 6 over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator x minus 4 over denominator x plus 2 end fraction end cell end table$

Invers dari f open parentheses x close parentheses didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator x minus 4 over denominator x plus 2 end fraction end cell row cell y open parentheses x plus 2 close parentheses end cell equals cell x minus 4 end cell row cell x y plus 2 y end cell equals cell x minus 4 end cell row cell x minus x y end cell equals cell 2 y plus 4 end cell row cell x open parentheses 1 minus y close parentheses end cell equals cell 2 y plus 4 end cell row x equals cell fraction numerator 2 y plus 4 over denominator 1 minus y end fraction end cell row blank blank blank row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 4 over denominator 1 minus x end fraction end cell end table$

Jadi, invers fungsi $f left parenthesis x minus 2 right parenthesis equals fraction numerator x minus 6 over denominator x end fraction$ adalah $fraction numerator 2 x plus 4 over denominator 1 minus x end fraction$ .