Questionand 12 , for the given functions $f$ and $g$, find the following: (c) $(f \cdot g)(x)$ (d) $\left(\frac{f}{g}\right)(x)$ (b) $(f-g)(x)$ (g) $(f \cdot g)(2)$ (h) $\left(\frac{f}{g}\right)(1)$ (f) $(f-g)(4)$
12. $f(x)=\frac{2 x+3}{3 x-2} ; g(x)=\frac{4 x}{3 x-2}$

Studdy Solution
Evaluate $(f - g)(4)$ by substituting $x = 4$ into $(f - g)(x)$.
$$(f - g)(4) = \frac{-2(4)+3}{3(4)-2} = \frac{-8+3}{12-2} = \frac{-5}{10} = -\frac{1}{2}$$
Solution Summary:
1. $(f \cdot g)(x) = \frac{8x^2 + 12x}{(3x-2)^2}$
2. $\left(\frac{f}{g}\right)(x) = \frac{2x+3}{4x}$
3. $(f - g)(x) = \frac{-2x+3}{3x-2}$
4. $(f \cdot g)(2) = \frac{7}{2}$
5. $\left(\frac{f}{g}\right)(1) = \frac{5}{4}$
6. $(f - g)(4) = -\frac{1}{2}$