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Diketahui  dan  adalah invers fungsi . Nilai dari ...

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 9 x plus 17 over denominator x plus 2 end fraction comma space x not equal to negative 2 end style dan begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style adalah invers fungsi begin mathsize 14px style f open parentheses x close parentheses end style. Nilai dari begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses end style adalah ....

Jawaban:

Dengan menggunakan konsep invers fungsi, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 9 x plus 17 over denominator x plus 2 end fraction end cell row y equals cell fraction numerator 9 x plus 17 over denominator x plus 2 end fraction end cell row cell y x plus 2 y end cell equals cell 9 x plus 17 end cell row cell y x minus 9 x end cell equals cell negative 2 y plus 17 end cell row cell x left parenthesis y minus 9 right parenthesis end cell equals cell negative 2 y plus 17 end cell row x equals cell fraction numerator negative 2 y plus 17 over denominator y minus 9 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 2 x plus 17 over denominator x minus 9 end fraction end cell row blank blank blank row cell f to the power of negative 1 end exponent left parenthesis 10 right parenthesis end cell equals cell fraction numerator negative 2 open parentheses 10 close parentheses plus 17 over denominator 10 minus 9 end fraction end cell row blank equals cell fraction numerator negative 20 plus 17 over denominator 1 end fraction end cell row blank equals cell negative 3 end cell end table end style

Jadi, nilai dari begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses equals negative 3 end style.

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