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

Oct 21, 2014

Consider the function $y = f \left(x\right)$

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.

$y = {x}^{2} / 2 + 4$
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.
$y = {x}^{2} / 2 + 4$

=> $y - 4 = {x}^{2} / 2$

=> $2 \left(y - 4\right) = {x}^{2}$

=> ${\left\{2 \left(y - 4\right)\right\}}^{\frac{1}{2}} = x$

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