Question

The domain of the function log√(3-x/2)
(a) (3, 0) (b) (-0,3)
(c) (0,3)​

Answer 1

Answer:

See below.

Step-by-step explanation:

We are given,

$f\left( x\right) =\log \left( \sqrt {\dfrac {3-x}{2}}\right)$

The logarithm of a negative number is undefined. So, the term,

$\begin{aligned}\sqrt {\dfrac {3-x}{2}} >0\Leftrightarrow \dfrac {3-x}{2} >0\\ \Rightarrow 3 >x\end{aligned}$

Hence, the domain is,

$x\in \left( -\infty ,3\right)$

Answer 2

Answer:(-0,3)

Step-by-step explanation:We are given,

f\left( x\right) =\log \left( \sqrt {\dfrac {3-x}{2}}\right)

The logarithm of a negative number is undefined. So, the term,

\begin{aligned}\sqrt {\dfrac {3-x}{2}} >0\Leftrightarrow \dfrac {3-x}{2} >0\\ \Rightarrow 3 >x\end{aligned}

Hence, the domain is,

x\in \left( -\infty ,3\right)