Question

Find the domain and range of the function:f(x)= √ 5-x-3Domain:Range:

Answer 1

domain: x<5

range: y<-3

Step-by-step explanation: i got it right!

Answer 2

We nee to find the Range of the following function:

`f(x)=-√(5-x)-3`

So we need to find all those numbers on the y-axis that are connected with the different values of the x-variable.

Notice that to start with, the square root is defined always a positive number (or zero), so it can provide always values that are larger than or equal to zero. Notice as well that there is a negative sign in front of it, so that makes our possible y values always smaller than or equal to zero.

on the other hand, we need to consider that there is a "-3" (subtraction of 3 units following that square root, therefore the total expression can be smaller than and equal to "0 - 3", which makes the answer for the range the following:

`\text{Range}=\left\lbrace y\right|y\leq-3\}`

Now for the Domain:

Recall that the Domain of a function is given by all the x-values for which the function is defined. In our case the only limitation we have is that of the square root, since the square root can only be calculated for values larger than or equal to zero.

So we need to have whatever is inside the root being larger than or equal to zero. That is:

`\begin{gathered} 5-x\ge0 \\ 5\ge x \\ x\leq5 \end{gathered}`

So this defines what x-values are allowed in our Domain:

`\text{Domain}=\left\lbrace x\right|x\leq5\}`