\(f\left(0\right)=\dfrac{b}{d}\Rightarrow f\left(f\left(0\right)\right)=0\Rightarrow f\left(\dfrac{b}{d}\right)=0\)

\(\Rightarrow\dfrac{\dfrac{ab}{d}+b}{\dfrac{cb}{d}+d}=0\Rightarrow b\left(a+d\right)=0\Rightarrow\left[{}\begin{matrix}b=0\\d=-a\end{matrix}\right.\)

TH1: \(b=0\)

\(f\left(1\right)=1\Rightarrow a=c+d\)

\(f\left(2\right)=2\Rightarrow2a=2\left(2c+d\right)\Rightarrow a=2c+d\) 

\(\Rightarrow2c+d=c+d\Rightarrow c=0\) (ktm)

TH2: \(d=-a\)

\(f\left(1\right)=1\Rightarrow a+b=c+d=c-a\Rightarrow2a+b=c\) (1)

\(f\left(2\right)=2\Rightarrow2a+b=2\left(2c+d\right)=2\left(2c-a\right)\Rightarrow4a+b=4c\) (2)

Trừ (2) cho (1) \(\Rightarrow2a=3c\Rightarrow\dfrac{a}{c}=\dfrac{3}{2}\)

\(\Rightarrow\lim\limits_{x\rightarrow\infty}\dfrac{ax+b}{cx+d}=\dfrac{a}{c}=\dfrac{3}{2}\)

Hay \(y=\dfrac{3}{2}\) là tiệm cận ngang

a ) Ta có : f(2) = 5 

\(\Leftrightarrow\hept{\begin{cases}f\left(x\right)=f\left(2\right)\\\text{ax}-3=5\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=2\\a.2-3=5\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=2\\a=4\end{cases}}\)

Vậy a = 4 

b ) Ta có : f(0) = 3

\(\Leftrightarrow\hept{\begin{cases}f\left(x\right)=f\left(0\right)\\\text{ax}+b=3\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=0\\a.0+b=3\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=0\\b=3\end{cases}}\) ( 1 ) 

Ta có : f ( 1 ) = 4 

\(\Leftrightarrow\hept{\begin{cases}f\left(x\right)=f\left(1\right)\\\text{ax}+b=4\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=1\\a.1+b=4\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=1\\a+b=4\end{cases}}\) ( 2 ) 

Thay b = 3 ở ( 1 ) vào a+b=4 ở ( 2 ) ta được : a + 3 = 4    

                                                                         a       = 1 

Vậy a = 1 ; b = 3 

Từ \(f\left(1\right)\le f\left(2\right)\)

\(\Rightarrow a+b\le2a+b\)

\(\Rightarrow a\ge0\)(1)

Từ \(f\left(5\right)\ge f\left(6\right)\)

\(\Rightarrow5a+b\ge6a+b\)

\(\Rightarrow a\le0\)(2)

Từ (1) và (2) => a = 0

Khi đó \(f\left(x\right)=0.a+b=b\)

Vì \(f\left(999\right)=1000\)

\(\Rightarrow b=1000\)

Khi đó \(f\left(2018\right)=b=1000\)

Vậy f(2018) = 1000 

Ta có :

\(f\left(1\right)=a-7=-4\)\(\Leftrightarrow a=3\)

\(f\left(2\right)=2a-7=5\Leftrightarrow a=6\)

\(f\left(3\right)=3a-7=6\Leftrightarrow a=\frac{13}{3}\)

2/3/4x = 3/1/7:0.01

k bn nha