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Question
The distance S object travel 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 constant. Verify whether the function S(t) is one-one or not.
Solution
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 value of t, there will be different values as images.
And there will be different pre-images for the different values of the range.
Therefore it is the one-one function.
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