Pertanyaan

Diketahui f ( x ) = 5 x + 2 1 dan g ( x ) = 4 3 x − 6 . Nilai ( g ∘ f ) − 1 ( − 5 ) = ....

Diketahui $f (x) = 5 x + \frac{1}{2}$ dan $g (x) = \frac{3}{4} x - 6$ . Nilai $(g \circ f)^{- 1} (- 5) =$ ....

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui dan . kita cari dlu fungsi komposisinya : kemudian kita tentukan inversnya : jadi, jawabannya E

Diketahui dan .

kita cari dlu fungsi komposisinya :

begin mathsize 14px style equals g open parentheses 5 x plus 1 half close parentheses equals 3 over 4 open parentheses 5 x plus 1 half close parentheses minus 6 equals 15 over 4 x plus 3 over 8 minus 6 equals 15 over 4 x minus 45 over 8 end style

kemudian kita tentukan inversnya :

$begin mathsize 14px style y equals 15 over 4 x minus 45 over 8 8 y equals 30 x minus 45 8 y plus 45 equals 30 x fraction numerator 8 y plus 45 over denominator 30 end fraction equals x open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 8 x plus 45 over denominator 30 end fraction left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 5 right parenthesis equals fraction numerator 8 open parentheses negative 5 close parentheses plus 45 over denominator 30 end fraction equals fraction numerator negative 40 plus 45 over denominator 30 end fraction equals 5 over 30 equals 1 over 6 end style$

jadi, jawabannya E