Pertanyaan

Tentukan invers dari fungsi f ( x ) = 4 2 x + 1 − 3 !

Tentukan invers dari fungsi $f (x) = \frac{2 x + 1 - 3}{4}$ !

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L. Marlina

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Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

f − 1 ( x ) = 8 x 2 + 1 .

f^{- 1} (x) = 8 x^{2} + 1

Pembahasan

Dengan demikian, f − 1 ( x ) = 8 x 2 + 1 .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator square root of 2 x plus 1 minus 3 end root over denominator 4 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator square root of 2 x minus 2 end root over denominator 4 end fraction end cell row blank rightwards double arrow cell y equals fraction numerator square root of 2 x minus 2 end root over denominator 4 end fraction end cell row cell square root of 2 x minus 2 end root end cell equals cell 4 y end cell row cell open parentheses square root of 2 x minus 2 end root close parentheses squared end cell equals cell open parentheses 4 y close parentheses squared end cell row cell 2 x minus 2 end cell equals cell 16 y squared end cell row cell 2 x end cell equals cell 16 y squared plus 2 end cell row x equals cell fraction numerator 16 y squared plus 2 over denominator 2 end fraction end cell row x equals cell 8 y squared plus 1 end cell row blank rightwards double arrow cell f to the power of negative 1 end exponent open parentheses x close parentheses equals 8 x squared plus 1 end cell end table end style$

Dengan demikian, $f^{- 1} (x) = 8 x^{2} + 1$ .