Question

Cho hàm số

Y = f (x) =2004.x

a, CMR :f (a+b) = f(a) + f(b)

c, tìm x để f(x) = x²

Answer 1

a, Ta có:

\(f\left(a\right)=2004a;f\left(b\right)=2004b;\\ f\left(a+b\right)=2004.\left(a+b\right)\)

\(f\left(a\right)+f\left(b\right)=2004a+2004b=2004.\left(a+b\right)\)

\(\Rightarrow f\left(a\right)+f\left(b\right)=f\left(a+b\right)\) (đpcm)

b, Ta có:

\(f\left(x\right)=x^2\\ \Rightarrow2004x=x^2\Rightarrow x=2004\)

Vậy x=2004 thì \(f\left(x\right)=x^2\)

Chúc bạn học tốt!!!

Answer 2

a) f (x) = 2004x

f (a) = 2004a

f (b) = 2004b

\(\Rightarrow\) f (a) + f (b) = 2004a + 2004b = 2004. (a+ b) (1)

f ( a+b ) = 2004. ( a+b ) (2)

Từ (1) và (2) \(\Rightarrow\) f (a+b ) = f (a) + f (b)