Let C be the curve given by the equation F(x, y) = 0. Suppose that this curve can be parametriced as a(t) = In (V+14 + 1 + +7 ), y(t) = \+14 + 1-+7 -2, where t E R. We are given the following section of Maple code and Maple output output that may help with the questions below. > (sqrt (t-14+1) -t^7) * (sqrt (t-14+1) +t*7) ; ( V+14 + 1 - 17) ( V+14 + 1 + + 7 ) (4) > simplify ($) ; (5) > simplify (diff (sqrt (t-14+1) -t^7-4, t) ) ; 7+6(-+7 +V+14+1 (6) > simplify (diff (In (sqrt (t^14+1)+t^7) , t) ) ; 7+6 (7) V+14+1 (a) In the box below, (i) explain why x(t) is increasing for all t E R, and (ii) by simplifying x(t) + x(-t), show that a is an odd function of t. Advice: You can use the equation numbers in the Maple output above to refer to particular results if you need them in your explanation. Q > Equation A - A- Ix BIUS X x Styles Font . . . Words: 0 (b) To find y as a function of , the first step is to find the inverse of the function x (t) . Express your answer for the inverse t() using hyperbolic functions and enter it in the box below. Syntax advice: Enter your answer in exact form. Use sinh (x) , cosh (x), tanh (x), coth (x) for sinha, cosh x, tanha, cotha. . For example, if you answer is t(x) = (tanh(28) ) 65 or t(x) = \tanh(x8), then you should enter (tanh (x^8) ) ^ (1/65) t(x) =