Pertanyaan

Tentukan f ( x ) jika: b. f ( 4 x − 1 ) = 2 x 4 x − 5

Tentukan $f (x)$ jika:

b. $f (\frac{x - 1}{4}) = \frac{4 x - 5}{2 x}$

W. Wati

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui: Fungsi Misal , maka: Substitusi ke persamaan seperti berikut: Ubah persamaan menjadi . Diperoleh: Maka, f ( x ) = 8 x + 2 16 x − 1 .

Diketahui:

Fungsi $begin mathsize 14px style f open parentheses fraction numerator x minus 1 over denominator 4 end fraction close parentheses equals fraction numerator 4 x minus 5 over denominator 2 x end fraction end style$

Misal $begin mathsize 14px style y equals fraction numerator x minus 1 over denominator 4 end fraction end style$ , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator x minus 1 over denominator 4 end fraction end cell row cell x minus 1 end cell equals cell 4 y end cell row x equals cell 4 y plus 1 end cell end table end style$

Substitusi ke persamaan $begin mathsize 14px style f open parentheses fraction numerator x minus 1 over denominator 4 end fraction close parentheses equals fraction numerator 4 x minus 5 over denominator 2 x end fraction end style$ seperti berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses fraction numerator x minus 1 over denominator 4 end fraction close parentheses end cell equals cell fraction numerator 4 x minus 5 over denominator 2 x end fraction end cell row cell f open parentheses y close parentheses end cell equals cell fraction numerator 4 open parentheses 4 y plus 1 close parentheses minus 5 over denominator 2 open parentheses 4 y plus 1 close parentheses end fraction end cell row cell f open parentheses y close parentheses end cell equals cell fraction numerator 16 y plus 4 minus 5 over denominator 8 y plus 2 end fraction end cell row cell f open parentheses y close parentheses end cell equals cell fraction numerator 16 y minus 1 over denominator 8 y plus 2 end fraction end cell end table end style$

Ubah persamaan menjadi .

Diperoleh:

$begin mathsize 14px style f open parentheses y close parentheses equals fraction numerator 16 y minus 1 over denominator 8 y plus 2 end fraction f open parentheses x close parentheses equals fraction numerator 16 x minus 1 over denominator 8 x plus 2 end fraction end style$

Maka, $f (x) = \frac{16 x - 1}{8 x + 2}$ .