Question

What is the domain and range of  

y=1/2x²+4?

Answer 1

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=x²/2+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=x²/2+4

=> y−4=x²/2

=> 2(y−4)=x²

=> {2(y−4)}½=x

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

The domain of this function is the set of all real numbers, i.e. ,  R.

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