# Let f (x) = –5x + 3 and g(x) = 6x – 2, how do you find f • g and its domain?

Jul 25, 2016

$\left(f \cdot g\right) \left(x\right) = - 2 \left(15 {x}^{2} - 14 x + 3\right) , x \in \mathbb{R}$.

#### Explanation:

Let ${D}_{f} \mathmr{and} {D}_{g}$ be the domains of the given funs. $f \mathmr{and} g$, resp.

We can easily see that, ${D}_{f} = {D}_{g} = \mathbb{R}$

Now, by defn. the fun. $f \cdot g$ is defined by, $\left(f \cdot g\right) \left(x\right) = f \left(x\right) \cdot g \left(x\right)$,

where, $x \in {D}_{f} \cap {D}_{g}$.

Since, ${D}_{f} \cap {D}_{g} = \mathbb{R}$, we have, #(f*g) : RR rarr RR, where,

$\left(f \cdot g\right) \left(x\right) = f \left(x\right) \cdot g \left(x\right) = \left(- 5 x + 3\right) \left(6 x - 2\right) = - 30 {x}^{2} + 10 x + 18 x - 6 = - 30 {x}^{2} + 28 x - 6$.

Thus, $\left(f \cdot g\right) \left(x\right) = - 2 \left(15 {x}^{2} - 14 x + 3\right) , x \in \mathbb{R}$.