Question

I need help with this pre calc question

Answer 1

`\boxed{\boxed{\pink{\bf\leadsto The \ domain \ of \ x \ will \ be \ (-\infty , +\infty) \ that \ is\ all \ real .}}}`

Explanation:

Firstly set the argument in which (x² + 3) is Greater than 0 , to see where the expression is defined .

`\bf \implies (x^2+3) > 0`

Now ,let's simplify this

`\bf \implies (x^2+3)>0 \\\\\bf\implies x^2 > 0 - 3 \\\\\bf\implies\boxed{\red{\bf x^2 > (-3) }}`

Since the left side has even Power , it is always positive for all real numbers.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

`\underline{\green{\bf Interval\ Notation :- }}`

`\bf ( - \infty , +\infty)`

That is
`\bf \{ x | x \in \mathbb{R} \}`

Hence option (b) is correct .