Jika k(x)=x+3x−2, x=−3, tentukan nilai dari ekspresi k−1(−1)⋅k−1(0).

Pertanyaan

Jika $begin mathsize 14px style k open parentheses x close parentheses equals fraction numerator x minus 2 over denominator x plus 3 end fraction comma space x not equal to negative 3 end style$ , tentukan nilai dari ekspresi $\style{font-size:14px}{k^{-1}\left(-1\right)\cdot k^{-1}\left(0\right)}$ .

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

Pembahasan

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

Misalkan , maka

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

Untuk , diperoleh

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

Sehingga

Jadi .