Suppose that the functions \( g \) and \( h \) are defined for all real numbers \( x \) as follows. \( \begin{array}{l}g(x)=3 x+3 \\ h(x)=x-1 \\ \text { Write the expressions for }(g \cdot h)(x) \text { and }(g-h)(x) \text { and evaluate }(g+h)(3) \text {. } \\ (g \cdot h)(x)=\square \\ (g-h)(x)=\square\end{array} \)

\( g(x)=3x+3 \quad \text{and} \quad h(x)=x-1. \) 1. To find \((g \cdot h)(x)\), multiply the functions: \[ (g \cdot h)(x)=g(x)\cdot h(x)=(3x+3)(x-1). \] Expanding, we have: \[ (3x+3)(x-1)=3x\cdot x+3x\cdot(-1)+3\cdot x+3\cdot(-1)=3x^2-3x+3x-3=3x^2-3. \] So, \[ (g \cdot h)(x)=3x^2-3. \] 2. To find \((g-h)(x)\), subtract the functions: \[ (g-h)(x)=g(x)-h(x)=(3x+3)-(x-1). \] Simplifying, we get: \[ (3x+3)-(x-1)=3x+3-x+1=2x+4. \] So, \[ (g-h)(x)=2x+4. \] 3. To evaluate \((g+h)(3)\), first find \(g(3)\) and \(h(3)\): \[ g(3)=3(3)+3=9+3=12, \] \[ h(3)=3-1=2. \] Adding these: \[ (g+h)(3)=g(3)+h(3)=12+2=14. \] Thus, the expressions and evaluation are: \[ \begin{array}{l} (g \cdot h)(x)=3x^2-3, \\ (g-h)(x)=2x+4, \\ (g+h)(3)=14. \end{array} \]