# Solution

• September 4th 2009, 07:33 AM
lehder
Solution
Hi everybody,

f is a positive and continuous function on $\mathbb{R}^+$ such as:

$\lim_{x \to +\infty} \frac{f(x)}{x}=1$.

I must show that the following equation: f(x)=x accepts least one solution in $\mathbb{R}^+$.

Can you help me please?

And thank you anyway.
• September 4th 2009, 07:48 AM
Plato
Quote:

Originally Posted by lehder
f is a positive and continuous function on $\mathbb{R}^+$ such as:
$\lim_{x \to +\infty} \frac{f(x)}{x}=1$.
I must show that the following equation: f(x)=x accepts least one solution in $\mathbb{R}^+$.

I must not be reading this correctly.
What if $f(x)=x+1$? Is it true?