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Suatu fungsi  didefinisikan dengan . Nilai  adalah...

Suatu fungsi begin mathsize 14px style f end style didefinisikan dengan begin mathsize 14px style 5 space f open parentheses x close parentheses plus 3 space f open parentheses 1 over x close parentheses equals 12 x end style. Nilai begin mathsize 14px style f open parentheses 6 close parentheses end style adalah ...

Jawaban:

begin mathsize 14px style 5 space f open parentheses x close parentheses plus 3 space f open parentheses 1 over x close parentheses equals 12 x end style

Substitusi begin mathsize 14px style x equals 6 end style sehingga diperoleh persamaan (1) berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 5 f open parentheses 6 close parentheses plus 3 f open parentheses 1 over 6 close parentheses end cell equals cell 12 open parentheses 6 close parentheses end cell row cell 5 f open parentheses 6 close parentheses plus 3 f open parentheses 1 over 6 close parentheses end cell equals cell 72 space space space space... left parenthesis 1 right parenthesis end cell end table end style 

Substitusi begin mathsize 14px style x equals 1 over 6 end style sehingga diperoleh persamaan (2) berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 5 f open parentheses 1 over 6 close parentheses plus 3 f open parentheses 6 close parentheses end cell equals cell 12 open parentheses 1 over 6 close parentheses end cell row cell 5 f open parentheses 1 over 6 close parentheses plus 3 f open parentheses 6 close parentheses end cell equals 2 row cell 3 f open parentheses 6 close parentheses plus 5 f open parentheses 1 over 6 close parentheses end cell equals cell 2 space space space space space... left parenthesis 2 right parenthesis end cell end table end style 

Dari persamaan (1) dan (2), dapat dilakukan eliminasi begin mathsize 14px style f open parentheses 1 over 6 close parentheses end style sehingga diperoleh 

begin mathsize 14px style table row cell 5 f open parentheses 6 close parentheses plus 3 f open parentheses 1 over 6 close parentheses equals 72 end cell cell open vertical bar cross times 5 close vertical bar end cell cell 25 f open parentheses 6 close parentheses plus 15 f open parentheses 1 over 6 close parentheses equals 360 end cell end table table row cell 3 f open parentheses 6 close parentheses plus 5 f open parentheses 1 over 6 close parentheses equals 2 space space end cell cell open vertical bar cross times 3 close vertical bar end cell cell bottom enclose 9 f open parentheses 6 close parentheses space space plus 15 f open parentheses 1 over 6 close parentheses equals 6 space space space space space space end enclose space minus end cell end table end style 

                                                                  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 16 f left parenthesis 6 right parenthesis end cell equals 354 row cell f open parentheses 6 close parentheses end cell equals cell 354 over 16 end cell row cell f open parentheses 6 close parentheses end cell equals cell 177 over 8 end cell end table end style 

Jadi, nilai begin mathsize 14px style f open parentheses 6 close parentheses equals 177 over 8 end style.

 

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