Pertanyaan

Diketahui f ( x ) = 4 x − 1 5 x + 2 , x  = 4 1 . Tentukan f − 1 ( − 1 ) !

Diketahui $f (x) = \frac{5 x + 2}{4 x - 1}, x \neq = \frac{1}{4}$ . Tentukan $f^{- 1} (- 1)$ !

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis equals fraction numerator negative 1 over denominator 9 end fraction end style$ .

Pembahasan

Menentukan invers dari fungsi rasional Menentukan nilai dari Jadi, nilai dari .

Menentukan invers dari fungsi rasional

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 5 x plus 2 over denominator 4 x minus 1 end fraction end cell row y equals cell fraction numerator 5 x plus 2 over denominator 4 x minus 1 end fraction end cell row cell y left parenthesis 4 x minus 1 right parenthesis end cell equals cell 5 x plus 2 end cell row cell 4 x y minus y end cell equals cell 5 x plus 2 end cell row cell 4 x y minus 5 x end cell equals cell y plus 2 end cell row cell x left parenthesis 4 y minus 5 right parenthesis end cell equals cell y plus 2 end cell row x equals cell fraction numerator y plus 2 over denominator 4 y minus 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator y plus 2 over denominator 4 y minus 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 2 over denominator 4 x minus 5 end fraction end cell row blank blank blank end table end style$

Menentukan nilai dari

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 2 over denominator 4 x minus 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis end cell equals cell fraction numerator left parenthesis negative 1 right parenthesis plus 2 over denominator 4 left parenthesis negative 1 right parenthesis minus 5 end fraction end cell row blank equals cell fraction numerator 1 over denominator negative 4 minus 5 end fraction end cell row blank equals cell fraction numerator 1 over denominator negative 9 end fraction end cell row blank equals cell negative 1 over 9 end cell end table end style$

Jadi, nilai dari $begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis equals fraction numerator negative 1 over denominator 9 end fraction end style$ .