jika f(x-2) = 1 per 2+5x, maka f' (x)

Jika f(x-2) = 1 per 2+5x, maka f' (x)

Pembahasan :

f(x - 2) = [tex] \frac{1}{2 + 5x} [/tex]

misal x - 2 = a

x = a + 2

f(a) = [tex] \frac{1}{2 + 5(a+2)} [/tex]

= [tex] \frac{1}{2 + 5a + 10} [/tex]

= [tex] \frac{1}{5a + 12} [/tex]

f(x) = [tex] \frac{1}{5x + 12} [/tex]

f'(x) = .. ?

[tex] \frac{1}{5x + 12} = y [/tex]

1 = y(5x + 12)

1 = 5xy + 12y

5xy = 1 - 12y

x = [tex] \frac{1 - 12y}{5y} [/tex]

f'(x) = [tex] \frac{1 - 12x}{5x} [/tex]

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kelas : 11

mapel : matematika

kategorisasi : fungsi

kata kunci : fungsi invers

kode : 11.2.2