Pertanyaan

Diketahui g ( x ) = x − 2 x + 1 , x  = 2 dan h ( x ) = x a x + 3 , x  = 0 . Tentukan nilai a yang memenuhi ( h ∘ g − 1 ) ( 4 ) = 6 .

Diketahui $g (x) = \frac{x + 1}{x - 2}, x \neq = 2$ dan $h (x) = \frac{a x + 3}{x}, x \neq = 0$ . Tentukan nilai $a$ yang memenuhi $(h \circ g^{- 1}) (4) = 6$ .

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

nilai yang memenuhi adalah .

nilai

yang memenuhi adalah

Pembahasan

Misalkan , maka Untuk , . dan . Maka Jadi nilai yang memenuhi adalah .

$begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator x plus 1 over denominator x minus 2 end fraction comma space x not equal to 2 end style$

Misalkan , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator x plus 1 over denominator x minus 2 end fraction end cell row cell y open parentheses x minus 2 close parentheses end cell equals cell x plus 1 end cell row cell x y minus 2 y end cell equals cell x plus 1 end cell row cell x y minus x end cell equals cell 2 y plus 1 end cell row cell x open parentheses y minus 1 close parentheses end cell equals cell 2 y plus 1 end cell row x equals cell fraction numerator 2 y plus 1 over denominator y minus 1 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 1 over denominator x minus 1 end fraction end cell end table end style$

Untuk

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent open parentheses 4 close parentheses end cell equals cell fraction numerator 2 open parentheses 4 close parentheses plus 1 over denominator open parentheses 4 close parentheses minus 1 end fraction end cell row blank equals cell fraction numerator 8 plus 1 over denominator 3 end fraction end cell row blank equals cell 9 over 3 end cell row blank equals 3 end table end style$

$begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator straight a x plus 3 over denominator x end fraction comma space x not equal to 0 end style$ , . dan . Maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis h ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis 4 right parenthesis end cell equals 6 row cell h open parentheses g to the power of negative 1 end exponent open parentheses 4 close parentheses close parentheses end cell equals 6 row cell h open parentheses 3 close parentheses end cell equals 6 row cell fraction numerator straight a open parentheses 3 close parentheses plus 3 over denominator open parentheses 3 close parentheses end fraction end cell equals 6 row cell fraction numerator 3 straight a plus 3 over denominator 3 end fraction end cell equals 6 row cell 3 straight a plus 3 end cell equals 18 row cell 3 straight a end cell equals 15 row straight a equals cell 15 over 3 end cell row straight a equals 5 end table end style$

Jadi nilai yang memenuhi adalah .