**1.5 Fungsi, SPM Praktis (Soalan Pendek)**

**Soalan 8:**

Cari fungsi songsangan $f(x)=\frac{3x+2}{5x+3}$

*Penyelesaian:*

$\begin{array}{l}\text{}f(x)=\frac{3x+2}{5x+3}\\ \text{katakan}y=\frac{3x+2}{5x+3}\\ y\left(5x+3\right)=3x+2\\ 5xy+3y=3x+2\\ 5xy-3x=2-3y\\ x\left(5y-3\right)=2-3y\\ x=\frac{2-3y}{5y-3}\\ {f}^{-1}\left(x\right)=\frac{2-3x}{5x-3}\to \overline{)\begin{array}{l}\text{tukar}y\text{kepada}x\\ \text{untukcari}{f}^{-1}\left(x\right)\text{}\end{array}}\end{array}$
**Soalan 9:**

(a) Jika *f* : *x* → *x* – 2, cari *f *^{-1} (5),

$\text{(b)Jika}f:x\to \frac{x+9}{x-5},\text{}x\ne 5,\text{cari}{f}^{-1}(3).$

*Penyelesaian:*

**(a)**

*f* (*x*) = *x*– 2

**Katakan ***y *= *f *^{-1 }(5)

*f* (*y*) = 5

*y* – 2 = 5

*y* = 7

oleh itu, *f *^{-1 }(5) = 7

**(b)**

$\begin{array}{l}f(x)=\frac{x+9}{x-5}\\ \text{katakan}y={f}^{-1}(3)\\ f(y)=3\\ \frac{y+9}{y-5}=3\\ y+9=3y-15\\ 2y=24\\ y=12\\ \therefore {f}^{-1}\left(3\right)=7\end{array}$