Answer
a. This is true.
b. This is also true.
Work Step by Step
Taking the derivative of the function, we get $2x$. This is greater than $0$, when $x>0$ and is less than $0$ when $x<0$, so the function is increasing on the set of all real numbers greater than zero and is decreasing on the set of all real numbers less than zero. The statement is proven.
