Pertanyaan

Tentukan invers dari fungsi di bawah ini: c. f ( x ) = x 2 − 10 , x ≥ 10

Tentukan invers dari fungsi di bawah ini:

c. $f (x) = x^{2} - 10, x \geq 10$

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R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

invers fungsi adalah .

invers fungsi f open parentheses x close parentheses equals x squared minus 10 comma space x greater or equal than 10

adalah $f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator square root of x plus 40 end root over denominator 2 end fraction$ .

Pembahasan

Diketahui fungsi . Invers fungsi tersebut sebagai berikut. atau Kemudian, diketahui bahwa , maka fungsi invers yang memenuhi yaitu . Dengan demikian, invers fungsi adalah .

Diketahui fungsi f open parentheses x close parentheses equals x squared minus 10 comma space x greater or equal than 10 . Invers fungsi tersebut sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator 0 plus-or-minus square root of 0 minus 4 times 1 times open parentheses negative 10 minus y close parentheses end root over denominator 2 times 1 end fraction end cell row blank equals cell fraction numerator plus-or-minus square root of 40 plus y end root over denominator 2 end fraction end cell row blank equals cell fraction numerator plus-or-minus square root of y plus 40 end root over denominator 2 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals cell fraction numerator square root of y plus 40 end root over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator square root of y plus 40 end root over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator square root of x plus 40 end root over denominator 2 end fraction end cell end table$ atau $table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 2 end cell equals cell fraction numerator negative square root of y plus 40 end root over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator negative square root of y plus 40 end root over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative square root of x plus 40 end root over denominator 2 end fraction end cell end table$

Kemudian, diketahui bahwa x greater or equal than 10 , maka fungsi invers yang memenuhi yaitu $f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator square root of x plus 40 end root over denominator 2 end fraction$ .

Dengan demikian, invers fungsi f open parentheses x close parentheses equals x squared minus 10 comma space x greater or equal than 10 adalah $f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator square root of x plus 40 end root over denominator 2 end fraction$ .