Pertanyaan

Diketahui f ( x ) = x + 2 5 x − 3 , x  = − 2 , tentukan: a. f − 1 ( x ) b. f − 1 ( 2 )

Diketahui $f (x) = \frac{5 x - 3}{x + 2}, x \neq = - 2$ , tentukan:

a. $f^{- 1} (x)$

b. $f^{- 1} (2)$

A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Ingat sifat invers : Dengan demikian, dan nilai dari .

Ingat sifat invers :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 5 x minus 3 over denominator x plus 2 end fraction end cell row y equals cell fraction numerator 5 x minus 3 over denominator x plus 2 end fraction end cell row cell y left parenthesis x plus 2 right parenthesis end cell equals cell 5 x minus 3 end cell row cell x y plus 2 y end cell equals cell 5 x minus 3 end cell row cell x y minus 5 x end cell equals cell negative 2 y minus 3 end cell row cell x left parenthesis y minus 5 right parenthesis end cell equals cell negative 2 y minus 3 end cell row x equals cell fraction numerator negative 2 y minus 3 over denominator y minus 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator negative 2 y minus 3 over denominator y minus 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator negative 2 x minus 3 over denominator x minus 5 end fraction end cell row blank blank blank row cell f to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell fraction numerator negative 2 left parenthesis 2 right parenthesis minus 3 over denominator 2 minus 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell fraction numerator negative 7 over denominator negative 3 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell 7 over 3 end cell end table$

Dengan demikian, $f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 2 x minus 3 over denominator x minus 5 end fraction$ dan nilai dari table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell 7 over 3 end cell end table .