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Diketahui fungsi , . Jika  adalah invers dari , ni...

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 7 x minus 5 over denominator 4 x plus 3 end fraction end stylebegin mathsize 14px style x not equal to negative 3 over 4 end style. Jika begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style adalah invers dari begin mathsize 14px style f open parentheses x close parentheses end style, nilai begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 2 close parentheses end style adalah ....

Jawaban:

Gunakan konsep invers fungsi.

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 7 x minus 5 over denominator 4 x plus 3 end fraction end stylebegin mathsize 14px style x not equal to negative 3 over 4 end style.

Akan ditentukan nilai begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 2 close parentheses end style.

Terlebih dahulu tentukan begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x close parentheses equals y end cell equals cell fraction numerator 7 x minus 5 over denominator 4 x plus 3 end fraction end cell row cell y open parentheses 4 x plus 3 close parentheses end cell equals cell 7 x minus 5 end cell row cell 4 x y plus 3 y end cell equals cell 7 x minus 5 end cell row cell 4 x y minus 7 x end cell equals cell negative 3 y minus 5 end cell row cell x open parentheses 4 y minus 7 close parentheses end cell equals cell negative 3 y minus 5 end cell row x equals cell fraction numerator negative 3 y minus 5 over denominator 4 y minus 7 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 3 x minus 5 over denominator 4 x minus 7 end fraction end cell end table end style 

Kemudian tentukan begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 2 close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 3 x minus 5 over denominator 4 x minus 7 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses 2 close parentheses end cell equals cell fraction numerator negative 3 open parentheses 2 close parentheses minus 5 over denominator 4 open parentheses 2 close parentheses minus 7 end fraction end cell row blank equals cell fraction numerator negative 6 minus 5 over denominator 8 minus 7 end fraction end cell row blank equals cell fraction numerator negative 11 over denominator 1 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses 2 close parentheses end cell equals cell negative 11 end cell end table end style 

Jadi, diperoleh begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 2 close parentheses equals negative 11 end style.

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