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Theo đề bài: \(f\left(x\right)=2x+3\)
\(\Rightarrow\left\{{}\begin{matrix}f\left(x_1\right)=2\times x_1+3\\f\left(x_2\right)=2\times x_2+3\end{matrix}\right.\)
\(\Rightarrow f\left(x_1\right)+f\left(x_2\right)=2\times x_1+3+2\times x_2+3=\left(2\times x_1+2\times x_2\right)+\left(3+3\right)\) \(=2\times\left(x_1+x_2\right)+6\) \(=2\times5+6=10+6=16\)
Vậy \(f\left(x_1\right)+f\left(x_2\right)=16\).
f(x1)+f(x2)= (2.x1+3)+(2.x2+3)=2.(x1+x2)+6=2.5+6=16
Bấm đúng nhé
Theo c) \(f\left(\frac{5}{7}\right)=f\left(\frac{2}{7}+\frac{3}{7}\right)=f\left(\frac{2}{7}\right)+f\left(\frac{3}{7}\right)\)
\(f\left(\frac{2}{7}\right)=f\left(\frac{1}{7}+\frac{1}{7}\right)=f\left(\frac{1}{7}\right)+f\left(\frac{1}{7}\right)=2.f\left(\frac{1}{7}\right)\)
\(f\left(\frac{3}{7}\right)=f\left(\frac{1}{7}+\frac{2}{7}\right)=f\left(\frac{1}{7}\right)+f\left(\frac{2}{7}\right)=f\left(\frac{1}{7}\right)+2f\left(\frac{1}{7}\right)=3.f\left(\frac{1}{7}\right)\)
\(\implies\)\(f\left(\frac{5}{7}\right)=5.f\left(\frac{1}{7}\right)\) (1)
Theo b) \(f\left(\frac{1}{7}\right)=\frac{1}{7^2}.f\left(7\right)\) (2)
Theo c) \(f\left(7\right)=f\left(3+4\right)=f\left(3\right)+f\left(4\right)\)
\(=2.f\left(3\right)+f\left(1\right)\)
\(=6.f\left(1\right)+f\left(1\right)\)
\(=7.f\left(1\right)\)
Theo a)\(f\left(1\right)=1\)\(\implies\)\(f\left(7\right)=7\) (3)
Từ (1);(2);(3)
\(\implies\) \(f\left(\frac{5}{7}\right)=\frac{5}{7}\)
