Roboguru

Perhatikan fungsi-fungsi berikut ini : (i) (ii)...

Perhatikan fungsi-fungsi berikut ini :

(i) begin mathsize 14px style f open parentheses x close parentheses equals x cubed minus 2 x end style

(ii) begin mathsize 14px style f open parentheses x close parentheses equals negative 3 x to the power of 5 end style

(iii) begin mathsize 14px style f open parentheses x close parentheses equals 6 x plus 2 end style

(iv) begin mathsize 14px style f open parentheses x close parentheses equals x to the power of 5 plus 4 x end style

(v) begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared plus 1 end style

Berdasarkan kelima fungsi di atas, yang merupakan fungsi genap adalah begin mathsize 14px style.... end style

  1. (i)space

  2. (ii)undefined

  3. (iii)undefined

  4. (iv)undefined

  5. (v)undefined

Jawaban:

Jika begin mathsize 14px style f open parentheses negative x close parentheses equals f open parentheses x close parentheses end style untuk setiap bilangan riil begin mathsize 14px style x end style, maka begin mathsize 14px style f open parentheses x close parentheses end style merupakan fungsi genap. Selanjutnya kita akan mengecek fungsi pada setiap opsi.

(i) begin mathsize 14px style f open parentheses x close parentheses equals x cubed minus 2 x end style

undefined

Karena begin mathsize 14px style f open parentheses negative x close parentheses not equal to f open parentheses x close parentheses end style, maka undefined bukan fungsi genap.

(ii) begin mathsize 14px style f open parentheses x close parentheses equals negative 3 x to the power of 5 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative x close parentheses end cell equals cell negative 3 open parentheses negative x close parentheses to the power of 5 end cell row blank equals cell 3 x to the power of 5 end cell end table end style

Karena undefined, maka undefined bukan fungsi genap

(iii) begin mathsize 14px style f open parentheses x close parentheses equals 6 x plus 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative x close parentheses end cell equals cell 6 open parentheses negative x close parentheses plus 2 end cell row blank equals cell negative 6 x plus 2 end cell end table end style

Karena undefined, maka undefined bukan fungsi genap.

(iv) begin mathsize 14px style f open parentheses x close parentheses equals x to the power of 5 plus 4 x end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative x close parentheses end cell equals cell open parentheses negative x close parentheses to the power of 5 plus 4 open parentheses negative x close parentheses end cell row blank equals cell negative x to the power of 5 minus 4 x end cell row blank equals cell negative open parentheses x to the power of 5 plus 4 x close parentheses end cell end table end style

Karena undefined, maka undefined bukan fungsi genap.

(v) begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared plus 1 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative x close parentheses end cell equals cell 2 open parentheses negative x close parentheses squared plus 1 end cell row blank equals cell 2 x plus 1 end cell end table end style

Karena undefined, maka undefined merupakan fungsi genap.

Jadi, jawaban yang tepat adalah E.

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