The distance S an object travels under the influence of gravity in time t seconds is given by S(t) = 1/2.gt^2 +at +bt where, (g is the acceleration due to gravity), a, b are constants. Check if the function S (t )is one-one type of function (injection/injective)
Answers
Answer:
Step-by-step explanation:
For a function to be one to one , each and every element in it should have a unique image, in this case for each and every value of time t, there should be an unique value of distance S, for this to happen or for a function to be injective it should either increase continuously or decrease continuously. Differentiating the given function with respect to time we get
gt+a+b
The function can be either increasing or decreasing depending on the values of constant a and b.
If a and b are positive the function is continuously increasing, therefore it is an injective function.
If a and b are negative the function is continuously decreasing till gt is less than a+b and increases after that , therefore it is not an injective function in this case.