Question

Proving $ \ f : \mathbb{R} \to \mathbb{R}$ $ f(x) = \begin{cases} \frac{1}{x-1} , x<1 \\ \sqrt{x-1} , x \ge 1 \end{cases}$ is a bijection

score 70 · Answer 1 · 2017-08-13 02:05:59

70

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Proving $ \ f : \mathbb{R} \to \mathbb{R}$ $ f(x) = \begin{cases} \frac{1}{x-1} , x<1 \\ \sqrt{x-1} , x \ge 1 \end{cases}$ is a bijection

Published on 13 Aug 2017 - 2:05

score 186 · Answer 2 · 2017-08-15 01:17:01

Use the $\epsilon$, $\delta$ definition of continuity to prove $f$ is continuous on $[-\infty,1)\cup (1,5]$ and that it is not continuous at $1$

score 55 · Answer 3 · 2017-08-15 20:06:08

55

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Solving a functional equation between restriction of a function in an interval

Published on 15 Aug 2017 - 20:06

score 1.6k · Answer 4 · 2017-09-01 02:17:19

1.6k

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Published on 01 Sep 2017 - 2:17

score 243 · Answer 5 · 2017-09-09 14:43:49

243

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Published on 09 Sep 2017 - 14:43

score 1.4k · Answer 6 · 2017-09-14 14:54:59

1.4k

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Published on 14 Sep 2017 - 14:54

score 251 · Answer 7 · 2017-09-28 14:23:00

251

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Published on 28 Sep 2017 - 14:23

score 2k · Answer 8 · 2026-03-25 14:19:13

2k

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Published on 25 Mar 2026 - 14:19

score 55 · Answer 9 · 2017-10-03 06:00:21

55

Views

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Published on 03 Oct 2017 - 6:00

score 48 · Answer 10 · 2017-10-03 06:20:25

48

Views

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Published on 03 Oct 2017 - 6:20

score 56 · Answer 11 · 2017-10-05 15:53:44

56

Views

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Published on 05 Oct 2017 - 15:53

score 113 · Answer 12 · 2017-10-11 11:29:07

113

Views

If $\gamma:[a,b]\rightarrow \mathbb{C}$ is a piecewise smooth path and if $\beta:[c,d]\rightarrow \mathbb{C}$ is a path that can be obtained from

Published on 11 Oct 2017 - 11:29

score 706 · Answer 13 · 2026-03-20 13:00:40

706

Views

Functional Square Root of Piecewise Functions

Published on 20 Mar 2026 - 13:00

score 28 · Answer 14 · 2017-10-20 14:36:53

28

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Published on 20 Oct 2017 - 14:36

score 4.4k · Answer 15 · 2017-10-23 01:43:34

4.4k

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Published on 23 Oct 2017 - 1:43

List Question

Proving $ \ f : \mathbb{R} \to \mathbb{R}$ $ f(x) = \begin{cases} \frac{1}{x-1} , x<1 \\ \sqrt{x-1} , x \ge 1 \end{cases}$ is a bijection

Use the $\epsilon$, $\delta$ definition of continuity to prove $f$ is continuous on $[-\infty,1)\cup (1,5]$ and that it is not continuous at $1$

Solving a functional equation between restriction of a function in an interval

Determine if g(f(x)) is continuous at x = 0

Differentiability Piecewise function

Derivative of a Continuous Piecewise Function

residue of piecewise holomorphic function

Initial value problem with piecewise right hand side

How would I solve the following question on continuity?

How would I solve for a?

Continuity of $f(x) = xy$ for $xy > 0$, $0$ otherwise

If $\gamma:[a,b]\rightarrow \mathbb{C}$ is a piecewise smooth path and if $\beta:[c,d]\rightarrow \mathbb{C}$ is a path that can be obtained from

Functional Square Root of Piecewise Functions

Finding values for which a piece-wise function is continuous

Addition of two piecewise function

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