# What is the domain of #f(x) = sqrt[cos(sinx)]#?

##### 2 Answers

all real numbers (

#### Explanation:

treat this as a composition of functions:

outer function:

middle function:

inner function:

work from outer function to inner:

for a value of x to produce a real output, the value in the

for

this means

now, the only restriction is that

so the domain is all real numbers (

We have our **radical function** given to us:

The **domain** is

Using the **Interval Notations**

#### Explanation:

We have our **radical function** given to us:

Please refer to the graph of this **radical function** below:

When we analyze the graph above, we observe that the given radical function does not have any **undefined points** and we also observe that three are no **domain constraints**.

Therefore,

The **domain** is

Using the **Interval Notations** we can write our **domain** as