4. Let f: R R to be a contiuous, strictly monotone function. Let f(R) = R. Thus its the inverse f-1 is defined on the whole real line R. Show that f-1: R R continous on R.

Calculus For The Life Sciences
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Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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4. Let f: R R to be a contiuous, strictly monotone function. Let f (R) = R.
Thus its the inverse f-1 is defined on the whole real line R. Show that f-1: R R
continous on R.
Hint: note Theorem 2.10 only deals with the case where the domain is a closed,
bounded interval. So you cannot apply it directly to problem 4. But you may follow
the proof of continuity of g(a) = V: [0, 00) [0, 00), which was considered as the
inverse of f(x) = : (0, 00) (0, 00).
1.
Transcribed Image Text:4. Let f: R R to be a contiuous, strictly monotone function. Let f (R) = R. Thus its the inverse f-1 is defined on the whole real line R. Show that f-1: R R continous on R. Hint: note Theorem 2.10 only deals with the case where the domain is a closed, bounded interval. So you cannot apply it directly to problem 4. But you may follow the proof of continuity of g(a) = V: [0, 00) [0, 00), which was considered as the inverse of f(x) = : (0, 00) (0, 00). 1.
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