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Tentukan invers fungsi f(x−2)=xx−6​.

Pertanyaan

Tentukan invers fungsi f left parenthesis x minus 2 right parenthesis equals fraction numerator x minus 6 over denominator x end fraction.

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

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 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.

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