Skip to main content
Mathematics

Return to Question

added 19 characters in body; edited tags
Source Link
Prem
Prem
  • 12.3k
  • 2
  • 16
  • 31

Let $f:\mathbb{R}\to\mathbb{R}$$ f : \mathbb{R} \to \mathbb{R} $ is a function such that $\forall x\in\mathbb{R}$ $$f(f(f(2x+3)))=x.$$ Show
$$ \forall x\in\mathbb{R} : f(f(f(2x+3)))=x $$
Show that $f$ is bijective.

We have to show that it$f$ is injective and surjective. 
How do we do that when we don't know what $f(x)$ is? We
We only have a strange looking equality that holds for all real $x$ and the domain of the function.

Let $f:\mathbb{R}\to\mathbb{R}$ is a function such that $\forall x\in\mathbb{R}$ $$f(f(f(2x+3)))=x.$$ Show that $f$ is bijective.

We have to show that it is injective and surjective. How do we do that when we don't know what $f(x)$ is? We only have a strange looking equality that holds for all real $x$ and the domain of the function.

Let $ f : \mathbb{R} \to \mathbb{R} $ is a function such that
$$ \forall x\in\mathbb{R} : f(f(f(2x+3)))=x $$
Show that $f$ is bijective.

We have to show that $f$ is injective and surjective. 
How do we do that when we don't know what $f(x)$ is?
We only have a strange looking equality that holds for all real $x$ and the domain of the function.

Source Link
Trifon
Trifon
  • 113
  • 6

Show that a function is $f$ bijective if $f(f(f(2x+3)))=x$ for all real $x$

Let $f:\mathbb{R}\to\mathbb{R}$ is a function such that $\forall x\in\mathbb{R}$ $$f(f(f(2x+3)))=x.$$ Show that $f$ is bijective.

We have to show that it is injective and surjective. How do we do that when we don't know what $f(x)$ is? We only have a strange looking equality that holds for all real $x$ and the domain of the function.