The distance S an object travels under the influence of gravity in time t seconds is given by S(t) = (1/2) gt2 + at + b where, (g is the acceleration due to gravity), a, b are constants. Check if the function S (t)is one-one.
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S(t) = (1/2) gt2 + at + b
Let t be 1, 2, 3, ..., seconds
S(1) = (1/2) g(12) + a(1) + b = (1/2) g + a + b
S(2) = (1/2) g(22) + a(2) + b = 2g + 2a + b
Yes, for every different values of t, there will be different values as images. And there will be different preimages for the different values of the range. Therefore it is one-one function.
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