Pertanyaan

Diketahui f ( x ) = 2 x − 3 dan ( g ∘ f ) ( x ) = 4 x − 9 . Nilai dari g − 1 ( 3 ) = …

Diketahui $f (x) = 2 x - 3 dan (g \circ f) (x) = 4 x - 9$ . Nilai dari $g^{- 1} (3) = \dots$

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari g to the power of negative 1 end exponent open parentheses 3 close parentheses equals 3

Pembahasan

Diketahui , maka didapatkan: Fungsi didapatkan: Nilai dari diapatkan: Jadi,nilai dari .

Diketahui f open parentheses x close parentheses equals 2 x minus 3 space dan space open parentheses g ring operator f close parentheses open parentheses x close parentheses equals 4 x minus 9 , maka g open parentheses x close parentheses didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 4 x minus 9 end cell row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell 4 x minus 9 end cell row cell g open parentheses 2 x minus 3 close parentheses end cell equals cell 4 x minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 4 open parentheses fraction numerator x plus 3 over denominator 2 end fraction close parentheses minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 2 open parentheses x plus 3 close parentheses minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x plus 6 minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x minus 3 end cell end table$

Fungsi g to the power of negative 1 end exponent open parentheses x close parentheses didapatkan:

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

Nilai dari g to the power of negative 1 end exponent open parentheses 3 close parentheses diapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent open parentheses 3 close parentheses end cell equals cell fraction numerator 3 plus 3 over denominator 2 end fraction end cell row blank equals cell 6 over 2 end cell row blank equals 3 end table$

Jadi, nilai dari g to the power of negative 1 end exponent open parentheses 3 close parentheses equals 3 .