ระดับความยาก 3.5/10
Ent'43 ถ้า f(x) = 4x และ g(x) = 2 / (x - 1) แล้วค่า x ที่ทำให้ (f o g)(x) = (g o f)(x) เท่ากับเท่าไร

เฉลย >> 0.2
ข้อนี้ต้องหาว่า (f o g)(x) และ (g o f)(x) เท่ากับอะไรก่อนครับ
(f o g)(x) = f(g(x)) = 4(2 / (x-1)) = 8 / (x - 1)
(g o f)(x) = g(f(x)) = 2 / (4x - 1)
ต่อไปก็ตั้งสมการครับแล้วก็แก้สมการครับ
(f o g)(x)     =     (g o f)(x)
8 / (x - 1)    =     2 / (4x - 1)
4(4x - 1)     =     x - 1
16x - 4        =     x - 1
15x              =     3
x                  =      1 / 5  
x                  =      0.2

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