Question

How do you find the domain of \[\sqrt {x + 4} \]?

Answer 1

Hint: Here we will write the equation and form a condition such that the given function must be greater than or equal to zero. Then by solving the equation, we will get the domain of the given function. The natural domain of a function is the range of the function where its value can lie.

Complete step by step solution:
So the given function is \[\sqrt {x + 4} \].
The domain of the given function must be greater than or equals to zero. Therefore, we get
\[ \Rightarrow x + 4 \geqslant 0\]
This condition is used to find the value of \[x\] which will give us the domain of the given function.
Now by solving the above equation we will get the domain of the function. Therefore, we get
\[ \Rightarrow x \geqslant - 4\]
So, the upper limit of the function is positive infinity i.e. \[ + \infty \].
Now we will write the domain of the function in the brackets. Therefore, we get
Domain \[ = \left[ { - 4, + \infty } \right)\].

Hence, the domain of the function \[\sqrt {x + 4} \] is equal to \[\left[ { - 4, + \infty } \right)\].

Note: We know that the value of any term inside the log function is always positive; it can never be negative. We can write the domain in bracket form. Also, we have to keep in mind the type of bracket that should be used to show the natural domain of the function.