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

1 Answer
Oct 8, 2017

Answer:

#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)#.