Tentukan fungsi invers dari !

Pertanyaan

Tentukan fungsi invers dari $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction comma space x not equal to 1 half end style$ !

Pembahasan Soal:

$begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction comma space x not equal to 1 half end style$ misalkan $begin mathsize 14px style f open parentheses x close parentheses equals y end style$ maka $begin mathsize 14px style x equals f to the power of negative 1 end exponent open parentheses y close parentheses end style$ sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction end cell row y equals cell fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction end cell row cell 2 x y minus y end cell equals cell 3 x plus 4 end cell row x equals cell fraction numerator negative y minus 4 over denominator 3 minus 2 y end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator negative y minus 4 over denominator 3 minus 2 y end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative x minus 4 over denominator 3 minus 2 x end fraction comma space x not equal to 3 over 2 end cell end table end style$

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Maret 2021

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