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is f(x) = x^3 - 6x^2 +15x + 3 an invertible fxn?

is f(x) = x^3 - 6x^2 +15x + 3 an invertible fxn?

Grade:12

1 Answers

mycroft holmes
272 Points
12 years ago

f'(x) = 3(x2-4x+5)>0. Hence f is strictly monotonic and hence injective

 

Now as x tends to infinity, f(x) tends to infinity and x tends to -infinity f(x) tends to - infinity. Since f(x) is continuous, it takes all real values. Hence f(x) is surjective

 

Hence f(x) is bijective and so it is invertible.

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