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Bila f open parentheses x close parentheses equals fraction numerator x plus 2 over denominator 3 minus x end fraction dengan x not equal to 3 maka invers dari f to the power of negative 1 end exponent open parentheses x close parentheses adalah ...

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Misalkan y equals f open parentheses x close parentheses maka berdasarkan konsep invers fungsi x equals f to the power of negative 1 end exponent open parentheses y close parentheses sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator x plus 2 over denominator 3 minus x end fraction end cell row y equals cell fraction numerator x plus 2 over denominator 3 minus x end fraction end cell row cell y open parentheses 3 minus x close parentheses end cell equals cell x plus 2 end cell row cell 3 y minus x y end cell equals cell x plus 2 end cell row cell negative x y minus x end cell equals cell 2 minus 3 y end cell row cell x open parentheses negative y minus 1 close parentheses end cell equals cell 2 minus 3 y end cell row x equals cell fraction numerator 2 minus 3 y over denominator negative y minus 1 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 2 minus 3 y over denominator negative y minus 1 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 2 minus 3 x over denominator negative x minus 1 end fraction comma space x not equal to negative 1 end cell end table 

 Dengan demikian invers dari f to the power of negative 1 end exponent open parentheses x close parentheses adalah f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 2 minus 3 x over denominator negative x minus 1 end fraction comma space x not equal to negative 1.

 

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