Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.1 : Review : Functions
32. Find the domain of \(Q\left( y \right) = \sqrt {{y^2} + 1} - \sqrt[3]{{1 - y}}\).
Show SolutionThe domain of this function will be the set of \(y\)’s that will work in both terms of this function. So, we need the domain of each of the terms.
For the first term let’s note that,
\[{y^2} + 1 \ge 1\]and so will always be positive. The domain of the first term is then all real numbers.
For the second term we need to notice that we’re dealing with the cube root in this case and we can plug all real numbers into a cube root and so the domain of this term is again all real numbers.
So, the domain of both terms is all real numbers and so the domain of the function as a whole must also be all real numbers or,
\[{\mbox{Domain : }} - \infty < y < \infty \]