Roboguru

Tentukan fungsi invers dari  dan  maka

Pertanyaan

Tentukan fungsi invers dari f dan f open parentheses a close parentheses equals fraction numerator log subscript 3 space a plus 3 over denominator 4 end fraction maka f to the power of negative 1 end exponent open parentheses 0 close parentheses equals.... 

Pembahasan Soal:

Misalkan f open parentheses a close parentheses equals y. Sehingga fungsi inversnya:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses a close parentheses end cell equals y row cell fraction numerator log subscript 3 space a plus 3 over denominator 4 end fraction end cell equals y row cell log subscript 3 space a plus 3 end cell equals cell 4 y end cell row cell log subscript 3 space a end cell equals cell 4 y minus 3 end cell row a equals cell 3 to the power of 4 y minus 3 end exponent end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell 3 to the power of 4 y minus 3 end exponent end cell row cell f to the power of negative 1 end exponent open parentheses a close parentheses end cell equals cell 3 to the power of 4 a minus 3 end exponent end cell end table 

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses 0 close parentheses end cell equals cell 3 to the power of 4 times 0 minus 3 end exponent end cell row blank equals cell 3 to the power of negative 3 end exponent end cell row blank equals cell 1 over 3 cubed end cell row blank equals cell 1 over 27 end cell end table  

Jadi, f to the power of negative 1 end exponent open parentheses 0 close parentheses equals 1 over 27.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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