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Diketahui fungsi . Invers fungsi dari  adalah ...

Pertanyaan

Diketahui fungsi f left parenthesis x right parenthesis equals fraction numerator 2 x over denominator 4 x plus 5 end fraction comma space x not equal to negative 5 over 4. Invers fungsi dari f left parenthesis x right parenthesis adalah ...

  1. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 5 x over denominator 4 x plus 2 end fraction comma space x not equal to negative 1 half 

  2. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative fraction numerator 5 x over denominator 2 x plus 4 end fraction comma space x not equal to negative 2 

  3. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 5 x over denominator 2 x plus 4 end fraction comma space x not equal to negative 2 

  4. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative fraction numerator 5 x over denominator 4 x minus 2 end fraction comma space x not equal to 1 half 

  5. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative fraction numerator 5 x over denominator 4 x minus 2 end fraction comma space x not equal to 1 half 

Pembahasan Soal:

Diketahui:

f left parenthesis x right parenthesis equals fraction numerator 2 x over denominator 4 x plus 5 end fraction comma space x not equal to negative 5 over 4

Mencari invers fungsi dari f left parenthesis x right parenthesis:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 2 x over denominator 4 x plus 5 end fraction end cell row cell y open parentheses 4 x plus 5 close parentheses end cell equals cell 2 x end cell row cell 4 x y plus 5 y end cell equals cell 2 x end cell row cell 4 x y minus 2 x end cell equals cell negative 5 y end cell row cell x open parentheses 4 y minus 2 close parentheses end cell equals cell negative 5 y end cell row x equals cell fraction numerator negative 5 y over denominator 4 y minus 2 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 negative 5 x over denominator 4 x minus 2 end fraction comma space x not equal to 1 half end cell end table 

Jadi, invers fungsi dari f left parenthesis x right parenthesis adalah f to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative fraction numerator 5 x over denominator 4 x minus 2 end fraction comma space x not equal to 1 half.

Dengan demikian, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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