Consider the following function. f (x ) = x - 12x + 35 X - 5 (a) Explain why f has a removable discontinuity at x = 5. (Select all that apply.) lim f(x) is finite. ( f(5) and lim f(x) are finite, but are not equal. x - 5 lim f(x) does not exists. O f(5) is undefined. O none of the above (b) Redefine f(5) so that f is continuous at x = 5 (and thus the discontinuity is "removed"). f(5) = Need Help? Read It [-/2 Points] DETAILS SCALCET9 2.5.029. Explain, using these theorems, why the function is continuous at every number in its domain. h ( t ) = cos ( tz) 1 - et O h(t) is the quotient of functions that are continuous on the domain of h(t), so it is continuous at every number in its domain. O h(t) is a polynomial, so it is continuous at every number in its domain. O h(t) is a logarithmic, so it is continuous at every number in its domain. O h(t) is a rational function, so it is continuous at every number in its domain. O h(t) is not continuous at every number in its domain. State the domain. (Enter your answer using interval notation.)