Pertanyaan

Jika f ( x ) = 3 x + 1 2 x − 3 , x  = − 3 1 dan g ( x ) = 2 x + 1 , maka ( f ∘ g ) − 1 ( x ) = ... .

Jika $f (x) = \frac{2 x - 3}{3 x + 1}, x \neq = - \frac{1}{3}$ dan $g (x) = 2 x + 1$ , maka $(f \circ g)^{- 1} (x) = ...$ .

R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh $begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 4 x plus 1 over denominator 4 minus 6 x end fraction space comma space x not equal to 4 over 6 end style$ .

Pembahasan

Diketahui: Terlebih dahulu mencari Perhatikan rumus cepat invers fungsi rasional berikut: Menentukan . Jadi, diperoleh .

Diketahui:

$begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 2 x minus 3 over denominator 3 x plus 1 end fraction comma space x not equal to negative 1 third end style$

Terlebih dahulu mencari

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses 2 x plus 1 close parentheses end cell row blank equals cell fraction numerator 2 open parentheses 2 x plus 1 close parentheses minus 3 over denominator 3 open parentheses 2 x plus 1 close parentheses plus 1 end fraction end cell row blank equals cell fraction numerator 4 x plus 2 minus 3 over denominator 6 x plus 3 plus 1 end fraction end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 4 x minus 1 over denominator 6 x plus 4 end fraction space comma space x not equal to negative 4 over 6 end cell end table end style$

Perhatikan rumus cepat invers fungsi rasional berikut:

$begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator a x plus b over denominator d x plus d end fraction rightwards double arrow f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative d x plus b over denominator c x minus a end fraction end style$

Menentukan .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses equals fraction numerator 4 x minus 1 over denominator 6 x plus 4 end fraction rightwards double arrow open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 4 x minus 1 over denominator 6 x minus 4 end fraction end cell row atau blank blank row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 4 x plus 1 over denominator 4 minus 6 x end fraction end cell end table end style$

Jadi, diperoleh $begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 4 x plus 1 over denominator 4 minus 6 x end fraction space comma space x not equal to 4 over 6 end style$ .

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