QuestionSuppose that the functions $f$ and $g$ are defined as follows. $\begin{array}{l} f(x) = -3x + 5 \\ g(x) = \sqrt{2x - 3} \end{array}$
Find $f \cdot g$ and $f+g$. Then, give their domains using interval notation.
$(f \cdot g)(x) = (-3x + 5)(\sqrt{2x - 3})$
Domain of $f \cdot g: \left[\frac{3}{2}, \infty\right)$
$(f+g)(x) =$ $\square$
Domain of $f+g$ : $\square$