Misalkan f(x)=x−22x+3 dan g(x)=5x+3, tentukanlah : ((f∘g)−1)−1(x)

Pertanyaan

Misalkan $begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator 2 straight x plus 3 over denominator straight x minus 2 end fraction end style$ dan $\style{font-size:14px}{\mathrm g\left(\mathrm x\right)=\sqrt{5\mathrm x+3}}$ , tentukanlah :

$\style{font-size:14px}{\left(\left(\mathrm f\circ\mathrm g\right)^{-1}\right)^{-1}\left(\mathrm x\right)}$

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style open parentheses open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 2 square root of 5 straight x plus 3 end root plus 3 over denominator square root of 5 straight x plus 3 end root minus 2 end fraction end style$

Pembahasan

Diketahui :
$begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator 2 straight x plus 3 over denominator straight x minus 2 end fraction end style$ dan ,

Ditanya : = ....

Penyelesaian :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis end cell row blank equals cell straight f left parenthesis straight g open parentheses straight x close parentheses right parenthesis end cell row blank equals cell fraction numerator 2 open parentheses straight g open parentheses straight x close parentheses close parentheses plus 3 over denominator straight g open parentheses straight x close parentheses minus 2 end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 5 straight x plus 3 end root close parentheses plus 3 over denominator square root of 5 straight x plus 3 end root minus 2 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style open parentheses open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 2 square root of 5 straight x plus 3 end root plus 3 over denominator square root of 5 straight x plus 3 end root minus 2 end fraction end style$