Tentukan rumus fungsi invers dari a. F(x)=5^2x+1 b. F(x)=3^-2x+4-5
Matematika
Cieka17
Pertanyaan
Tentukan rumus fungsi invers dari
a. F(x)=5^2x+1
b. F(x)=3^-2x+4-5
a. F(x)=5^2x+1
b. F(x)=3^-2x+4-5
1 Jawaban
-
1. Jawaban yosua107
a. f(x) = 5^2x + 1
=> y = 5^2x + 1
=> y - 1 = 5^2x
=> log(y-1) = log5^2x
=> log(y-1) = 2x log5
=> 5'log(y-1) = 2x
=> x = 5'log(y-1)
=> f invers x = 5'log(x-1)
b. f(x) = 3^-2x+4 - 5
=> y = 3^-2x+4 - 5
=> y+5 = 3^-2x+4
=> log(y+5) = log(3^-2x+4)
=> log(y+5) = -2x+4 log3
=> 3'log(y+5)= -2x+4
=> 3'log(y+5) - 4 = -2x
=> x = 4 - 3'log(y+5)
f invers x = 4 - 3'log(x+5)