Fara here are some answers..however you didn't show us any work...
do not expect us to do your home work...you have to do it by yourself and we will help you.
a) no it is not ....why? does your function passes the horizontal line test? if yes it is but here.....check it...
b+c) the inverse function can be found only if you get t<=2 or t> =2 which is the line of symmetry of the parabola h=64t-16t^2
for t<=2 then the inverse is t=2-sqr[(64-h)/16} while for t>=2 the inverse is t=2+sqr[(64-h)/16}
How to find this? revise the quadratic function and check how you complete the square and transform your function into completed square form...if you are an I/G student you have studied this in Gr-11. if you have no idea what i am talking about please visit this page :Completing the square - Wikipedia, the free encyclopedia
d+e) get the appropriate inverse functions and substitute the value of h to get what you need.