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Pertanyaan

Tentukan rumus fungsi invers dari f open parentheses x close parentheses equals fraction numerator 5 x plus 2 over denominator 4 x minus 1 end fraction dan tentukan nilai dari f to the power of negative 1 end exponent open parentheses negative 1 close parentheses!

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

invers dari f open parentheses x close parentheses equals fraction numerator 5 x plus 2 over denominator 4 x minus 1 end fraction adalah f to the power of negative 1 end exponent open parentheses x close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x plus 2 over denominator 4 x minus 5 end fraction end cell end table dan f to the power of negative 1 end exponent open parentheses negative 1 close parentheses equals negative 1 over 9.

Pembahasan

Menentukan invers dari fungsi rasional f(x) tersebut adalah sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f open parentheses x close parentheses end cell row y equals cell fraction numerator 5 x plus 2 over denominator 4 x minus 1 end fraction end cell row cell y open parentheses 4 x minus 1 close parentheses end cell equals cell 5 x plus 2 end cell row cell 4 x y minus y end cell equals cell 5 x plus 2 end cell row cell 4 x y minus 5 x end cell equals cell y plus 2 end cell row cell x open parentheses 4 y minus 5 close parentheses end cell equals cell y plus 2 end cell row x equals cell fraction numerator y plus 2 over denominator 4 y minus 5 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y plus 2 over denominator 4 y minus 5 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 2 over denominator 4 x minus 5 end fraction end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses negative 1 close parentheses end cell equals cell fraction numerator negative 1 plus 2 over denominator 4 open parentheses negative 1 close parentheses minus 5 end fraction end cell row blank equals cell fraction numerator 1 over denominator negative 4 minus 5 end fraction end cell row blank equals cell negative 1 over 9 end cell end table 

Dengan demikian, invers dari f open parentheses x close parentheses equals fraction numerator 5 x plus 2 over denominator 4 x minus 1 end fraction adalah f to the power of negative 1 end exponent open parentheses x close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x plus 2 over denominator 4 x minus 5 end fraction end cell end table dan f to the power of negative 1 end exponent open parentheses negative 1 close parentheses equals negative 1 over 9.

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