Question

If $f:R→R, g:R→R$ are continuous bijective, then prove/disprove $h(x)=f(x)−g(x)$ is a bijection function.

score 314 · Answer 1 · 2026-03-25 06:06:53

314

Views

If $f:R→R, g:R→R$ are continuous bijective, then prove/disprove $h(x)=f(x)−g(x)$ is a bijection function.

Published on 25 Mar 2026 - 6:06

score 81 · Answer 2 · 2026-03-28 15:01:37

81

Views

Continuous function defined in spheres

Published on 28 Mar 2026 - 15:01

score 408 · Answer 3 · 2026-03-28 06:40:56

408

Views

Baby Rudin Theorem 5.15 (Taylor's Theorem) continuity requirement

Published on 28 Mar 2026 - 6:40

score 26 · Answer 4 · 2018-06-03 12:05:01

26

Views

Question on Continuity of a function

Published on 03 Jun 2018 - 12:05

score 930 · Answer 5 · 2018-06-03 13:04:25

930

Views

Show that the supremum of a sequence of continuous functions is continuous

Published on 03 Jun 2018 - 13:04

score 443 · Answer 6 · 2018-06-03 15:36:45

443

Views

If $f:\mathbb{R}\to\mathbb{R}$ is continuous and is an additive homomorphism then $f(x)=f(1)x$

Published on 03 Jun 2018 - 15:36

score 4k · Answer 7 · 2026-03-25 04:40:21

4k

Views

Is the pre-image of a Borel set by a continuous function a Borel set? Is it an open set?

Published on 25 Mar 2026 - 4:40

score 47 · Answer 8 · 2018-06-04 02:26:56

47

Views

Checking the continuity and differentiability of a function defined on a non-connected set of $\mathbb{R}$

Published on 04 Jun 2018 - 2:26

score 53 · Answer 9 · 2018-06-04 04:12:01

53

Views

Let $f\colon\mathbb{R}\to\mathbb{R}$ be continuous. If $f(r)=0$ for $r\in\mathbb{Q}$. Show that $f=0$.

Published on 04 Jun 2018 - 4:12

score 35 · Answer 10 · 2018-06-04 07:25:26

If the derivative of a function is positive (or negative) at all points except at $x=a$, where it is zero, then monotoncity of function at $x=a$.

score 61 · Answer 11 · 2026-03-25 06:04:08

61

Views

Prove: If a continuous function is monotonic in $(a, b) $ then it is monotonic in $[a, b] $

Published on 25 Mar 2026 - 6:04

score 1k · Answer 12 · 2018-06-04 09:33:10

1k

Views

If $f(x)$ and $g(x)$ are continuous at $x=c$ then show that: $f(g(x))$ and $g(f(x))$ are also continuous at $x=c$.

Published on 04 Jun 2018 - 9:33

score 518 · Answer 13 · 2018-06-04 10:30:16

518

Views

Find all differentiable functions which satisfy following property:

Published on 04 Jun 2018 - 10:30

score 71 · Answer 14 · 2018-06-04 15:31:23

71

Views

Continuity of a piecewise function - considering paths

Published on 04 Jun 2018 - 15:31

score 66 · Answer 15 · 2026-03-25 09:29:06

66

Views

function $f$ is continuous in $[0,\infty)$ and $\displaystyle\lim_{x \to \infty} f(x) = f(0)$, prove that $f$ is not injective in $[0,\infty)$

Published on 25 Mar 2026 - 9:29

List Question

If $f:R→R, g:R→R$ are continuous bijective, then prove/disprove $h(x)=f(x)−g(x)$ is a bijection function.

Continuous function defined in spheres

Baby Rudin Theorem 5.15 (Taylor's Theorem) continuity requirement

Question on Continuity of a function

Show that the supremum of a sequence of continuous functions is continuous

If $f:\mathbb{R}\to\mathbb{R}$ is continuous and is an additive homomorphism then $f(x)=f(1)x$

Is the pre-image of a Borel set by a continuous function a Borel set? Is it an open set?

Checking the continuity and differentiability of a function defined on a non-connected set of $\mathbb{R}$

Let $f\colon\mathbb{R}\to\mathbb{R}$ be continuous. If $f(r)=0$ for $r\in\mathbb{Q}$. Show that $f=0$.

If the derivative of a function is positive (or negative) at all points except at $x=a$, where it is zero, then monotoncity of function at $x=a$.

Prove: If a continuous function is monotonic in $(a, b) $ then it is monotonic in $[a, b] $

If $f(x)$ and $g(x)$ are continuous at $x=c$ then show that: $f(g(x))$ and $g(f(x))$ are also continuous at $x=c$.

Find all differentiable functions which satisfy following property:

Continuity of a piecewise function - considering paths

function $f$ is continuous in $[0,\infty)$ and $\displaystyle\lim_{x \to \infty} f(x) = f(0)$, prove that $f$ is not injective in $[0,\infty)$

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