Bab 1 Fungsi

$\begin{array}{l}f\left(x\right)=\frac{mx-n}{x-2}\\ \text{Katakan }y=\frac{mx-n}{x-2}\to \boxed{\text{cari }{f}^{-1}\left(x\right)}\\ y\left(x-2\right)=mx-n\\ xy-2y=mx-n\\ xy-mx=2y-n\to \boxed{\begin{array}{l}\text{pindah }x\text{ ke }\\ \text{sebelah kiri}\end{array}}\end{array}$
$\begin{array}{l}x\left(y-m\right)=2y-n\\ x=\frac{2y-n}{y-m}\\ f^{-1}\left(x\right)=\frac{2x-n}{x-m}\\ \frac{2x-n}{x-m}=\frac{5-2x}{2-x}\to \boxed{\begin{array}{l}\text{bandingkan dengan}\\ f^{-1}\left(x\right)\text{ yang diberi}\end{array}}\\ \boxed{\times \frac{-1}{-1}}\frac{n-2x}{m-x}=\frac{5-2x}{2-x}\\ \text{maka, }n=5,m=2\end{array}$

$\begin{array}{l}f\left(x\right)=\frac{2h}{x-3k}\\ \text{Katakan }y=\frac{2h}{x-3k}\to \boxed{\text{cari }{f}^{-1}\left(x\right)}\\ y\left(x-3k\right)=2h\\ xy-3ky=2h\\ xy=2h+3ky\\ x=\frac{2h+3ky}{y}\end{array}$
$\begin{array}{l}{f}^{-1}\left(x\right)=\frac{2h+3kx}{x}\\ \frac{2h+3kx}{x}=\frac{14+24x}{x}\to \boxed{\begin{array}{l}\text{bandingkan dengan}\\ f^{-1}\left(x\right)\text{ yang diberi}\end{array}}\\ 2h=143k=24\\ h=7k=8\end{array}$