What is the domain and range of #y=1/2x^2+4#?

1 Answer
Oct 21, 2014

Consider the function #y= f(x)#

The domain of this function is all the values of x for which the function holds. The range is all those values of y for which the function is valid.

Now, coming to your question.
#y = x^2 / 2 + 4#
This function is valid for any real value of x. Thus the domain of this function is the set of all real numbers, i.e. , #R#.

Now, separate out x.
#y= x^2 /2 +4#

=> #y-4 = x^2 /2#

=> #2(y-4) = x^2#

=> #{2(y-4)}^(1/2) = x#

Thus, the function is valid for all real numbers greater than or equal to 4. Therefore the range of this function is [4, #oo#).