How do I prove that f(x)=x2−4x+3 is injective at (−∞,2) and (2,∞)
How do I prove that is injective at and
Answer & Explanation
Beginner2022-01-13Added 37 answers
This is true if and only if or .
Now if , then , so the only possibility is . Same for (try).
Beginner2022-01-14Added 37 answers
On the on the interval , we have
suppose that , then we have
but we know that both , a contradiction. Similar for the interval .
Skilled2022-01-24Added 366 answers
Step 1This real valued function is obiously continuous and differentiable at every point in ..So,and,.So since f is properly monotonous and coninouous in those two specific intervals, is also injective, i.e. if then .
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