Question

Hello! Was wondering what is the domain of this problem and the domains restriction with a one sentence explanation. Thank you!

Answer 1

Solution

$\begin{gathered} Given \\ \frac{-10t^2+50t}{t^2+4t+3} \\ \end{gathered}$$\begin{gathered} \frac{-10t^2+50t}{t^2+4t+3}\text{ =}\frac{-10t^2+50t}{t^2+3t+t+3} \\ =\frac{-10t^2+50t}{t(t+3)+1(t+3)} \\ =\frac{-10t^2+50t}{(t+3)(t+1)} \end{gathered}$

Set the denominator to zero

$\begin{gathered} (t+3)(t+1)=0 \\ t+3=0,\text{ or t+1=0} \\ t=-3\text{ or t=-1} \end{gathered}$

The domain of a function is the set of input values for which the function is real and defined.

Thus, the domain of the function is

t < -3, or -3 < t < -1 or t > -1

The domain restrictions are the value of t for which the function is undefined or not real

Thus, The domains restriction is t = -3 or t = -1