Roboguru

Jika diketahui   Maka nilai  adalah ....

Pertanyaan

Jika diketahui

f open parentheses fraction numerator 2 x plus 4 over denominator x plus 2 end fraction close parentheses equals x minus 1 comma space x not equal to negative 2 

Maka nilai f to the power of negative 1 end exponent open parentheses 0 close parentheses adalah ....

Pembahasan Soal:

Misalkan u equals fraction numerator 2 x plus 4 over denominator x plus 2 end fraction, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell u open parentheses x plus 2 close parentheses end cell equals cell 2 x plus 4 end cell row cell u x plus 2 u end cell equals cell 2 x plus 4 end cell row cell u x minus 2 x end cell equals cell negative 2 u plus 4 end cell row cell x open parentheses u minus 2 close parentheses end cell equals cell negative 2 u plus 4 end cell row x equals cell fraction numerator negative 2 u plus 4 over denominator u minus 2 end fraction end cell end table 

Rumus fungsi f open parentheses x close parentheses dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses fraction numerator 2 x plus 4 over denominator x plus 2 end fraction close parentheses end cell equals cell x minus 1 end cell row cell f open parentheses u close parentheses end cell equals cell fraction numerator negative 2 u plus 4 over denominator u minus 2 end fraction minus 1 end cell row blank equals cell fraction numerator negative 2 u plus 4 over denominator u minus 2 end fraction minus fraction numerator u minus 2 over denominator u minus 2 end fraction end cell row blank equals cell fraction numerator negative 2 u plus 4 minus u plus 2 over denominator u minus 2 end fraction end cell row blank equals cell fraction numerator negative 3 u plus 6 over denominator u minus 2 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator negative 3 x plus 6 over denominator x minus 2 end fraction end cell end table 

Dengan menerapkan konsep invers fungsi diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator negative 3 x plus 6 over denominator x minus 2 end fraction end cell row y equals cell fraction numerator negative 3 x plus 6 over denominator x minus 2 end fraction end cell row cell y open parentheses x minus 2 close parentheses end cell equals cell negative 3 x plus 6 end cell row cell x y minus 2 y end cell equals cell negative 3 x plus 6 end cell row cell x y plus 3 x end cell equals cell 2 y plus 6 end cell row cell x open parentheses y plus 3 close parentheses end cell equals cell 2 y plus 6 end cell row x equals cell fraction numerator 2 y plus 6 over denominator y plus 3 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 2 x plus 6 over denominator x plus 3 end fraction end cell end table 

Selanjutnya, dengan cara substitusi diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 6 over denominator x plus 3 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses 0 close parentheses end cell equals cell fraction numerator 2 open parentheses 0 close parentheses plus 6 over denominator 0 plus 3 end fraction end cell row blank equals cell 6 over 3 end cell row blank equals 2 end table 

Jadi, nilai f to the power of negative 1 end exponent open parentheses 0 close parentheses adalah 2.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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