Roboguru

Diketahui . Invers dari adalah...

Pertanyaan

Diketahui begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals 4 straight x plus 2 space dan space straight g left parenthesis straight x right parenthesis equals fraction numerator straight x minus 3 over denominator straight x plus 1 end fraction comma straight x not equal to negative 1 end style. Invers dari begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end style adalah...

  1. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 4 x plus 1 over denominator 3 x plus 4 end fraction comma x not equal to negative 4 over 3 end style

  2. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator negative 3 x plus 4 end fraction comma x not equal to negative 4 over 3 end style

  3. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x minus 1 over denominator 4 x plus 4 end fraction comma x not equal to negative 1 end style

  4. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x plus 1 over denominator 4 minus 4 x end fraction comma x not equal to 1 end style

  5. begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x plus 4 over denominator 4 x plus 4 end fraction comma x not equal to negative 1 end style

Pembahasan Soal:

Pertama tentukan fungsi begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g open parentheses 4 x plus 2 close parentheses end cell row blank equals cell fraction numerator 4 x plus 2 minus 3 over denominator 4 x plus 2 plus 1 end fraction end cell row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x minus 1 over denominator 4 x plus 3 end fraction end cell end table end style

Selanjutnya, invers fungsi begin mathsize 14px style y equals fraction numerator a x plus b over denominator c x plus d end fraction rightwards arrow y to the power of negative 1 end exponent equals fraction numerator negative d x plus b over denominator c x minus a end fraction end style

sehingga, invers fungsi begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end style yaitu

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator 4 x plus 3 end fraction rightwards arrow open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 3 x minus 1 over denominator 4 x minus 4 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 x plus 1 over denominator 4 minus 4 x end fraction end style

Jadi, jawaban yang tepat adalah D.   

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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