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Tentukan invers dari f(x)=3x+2​−4​!

Pertanyaan

Tentukan invers dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator square root of x plus 2 end root minus 4 over denominator 3 end fraction end style!

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

 invers dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator square root of x plus 2 end root minus 4 over denominator 3 end fraction end style adalah table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell 9 x squared plus 24 x plus 14 end cell end table.

Pembahasan

Pada fungsi f left parenthesis x right parenthesis equals y, dapat ditentukan fungsi inversnya dengan menggunakan operasi aljabar sedemikian hingga didapatkan f to the power of negative 1 end exponent left parenthesis x right parenthesis equals x seperti berikut

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 square root of x plus 2 end root minus 4 over denominator 3 end fraction end cell row blank rightwards double arrow cell y equals fraction numerator square root of x plus 2 end root minus 4 over denominator 3 end fraction end cell row cell 3 y end cell equals cell square root of x plus 2 end root minus 4 end cell row blank rightwards double arrow cell square root of x plus 2 end root equals 3 y plus 4 end cell row cell open parentheses square root of x plus 2 end root close parentheses squared end cell equals cell open parentheses 3 y plus 4 close parentheses squared end cell row cell x plus 2 end cell equals cell 9 y squared plus 24 y plus 16 end cell row x equals cell 9 y squared plus 24 y plus 16 minus 2 end cell row x equals cell 9 y squared plus 24 y plus 14 end cell row blank rightwards double arrow cell f to the power of negative 1 end exponent open parentheses x close parentheses equals 9 x squared plus 24 x plus 14 end cell end table end style 

Dengan demikian, invers dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator square root of x plus 2 end root minus 4 over denominator 3 end fraction end style adalah table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell 9 x squared plus 24 x plus 14 end cell end table.

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