Question

Cho: 2f(x)+3×f(1/x)=2x-1.

Tính f(2).

Giúp mk vs thanks.

Answer 1

Lời giải:

Thay $x=2$ ta có:

$2f(2)+3f(\frac{1}{2})=2.2-1=3$

$\Rightarrow 4f(2)+6f(\frac{1}{2})=6(1)$

Thay $x=\frac{1}{2}$ ta có:

$2f(\frac{1}{2})+3f(2)=2.\frac{1}{2}-1=0$

$\Rightarrow 6f(\frac{1}{2})+9f(2)=0(2)$

Lấy $(2)$ trừ $(1)$ suy ra: $5f(2)=-6\Rightarrow f(2)=\frac{-6}{5}$

Answer 2

Lời giải:

Thay $x=2$ ta có:

$2f(2)+3f(\frac{1}{2})=2.2-1=3$

$\Rightarrow 4f(2)+6f(\frac{1}{2})=6(1)$

Thay $x=\frac{1}{2}$ ta có:

$2f(\frac{1}{2})+3f(2)=2.\frac{1}{2}-1=0$

$\Rightarrow 6f(\frac{1}{2})+9f(2)=0(2)$

Lấy $(2)$ trừ $(1)$ suy ra: $5f(2)=-6\Rightarrow f(2)=\frac{-6}{5}$