Question

How do you find the domain and range of `f(x) = x+2`?

Answer 1

`x` belongs to Real numbers and `f(x)` belongs to Real numbers too. That means that the domain belongs to `RR` and the range belongs to `RR`.

Explanation:

The domain of a function are those values of `x` where we get defined values of `y` or `f(x)` . The range of a function are those values of `y` or `f(x)` we get when `x` is in the domain.

If we take your example into consideration->

`f(x)=x+2`

Here, we can let `x` be any real number and we would get a defined value for `f(x)` .

Therefore Domain is R and Range is R.

The same cannot be said for other functions.

For example-->

Let `f(x)=(x+2)^(1/2)`

If there is a negative number inside the root the function will not be defined. So we apply a condition-->

`x+2>=0`

Therefore
`x>=-2`

THIS IS THE DOMAIN. The value of `x` has to be bigger than or equal to `(-2)`

Now for the range, we'll put `x=-2` in the function.

We get `f(x)=0`

Remember the value of `x` always has to be bigger than or equal to `-2`. We can let any other number bigger than `-2` be in the domain.

So when we put any other number (bigger than `-2`) in `f(x)`
we will get values ranging till Infinity.

Therefore, the Range is `f(x)in[0, oo)`.