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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 begin mathsize 14px style k to the power of negative 1 end exponent open parentheses negative 1 close parentheses times k to the power of negative 1 end exponent open parentheses 0 close parentheses end style

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style k to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis times k to the power of negative 1 end exponent left parenthesis 0 right parenthesis equals negative 1 end style

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 begin mathsize 14px style y equals k open parentheses x close parentheses end style, 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 begin mathsize 14px style x equals negative 1 space dan space x equals 0 end style, 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 

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 times k to the power of negative 1 end exponent open parentheses 0 close parentheses end cell equals cell open parentheses negative 1 half close parentheses times open parentheses 2 close parentheses end cell row blank equals cell negative 1 end cell end table end style 

Jadi begin mathsize 14px style k to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis times k to the power of negative 1 end exponent left parenthesis 0 right parenthesis equals negative 1 end style

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