Let f he a function with domain IR1 with the following four properties: a f is oontinuous on its entire domain. 1- lim f(:12)= T. III3'00 1- lim f[:13)= 10. I f(2) = 1. Answer the following questions about f. {a} Prove that f has at least two roots. (Recall: a function g is said to have a root at a point a in its domain if Me) = CI.) {b} Is it necessarin true that f achieves a minimum value? If you believe this is true, prove it. If you believe it is false, provide a counterexample and explain Why it works