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Complex Functions Examples
I was asked to give an example of a function:
i) whose domain isn't equal to its codomain
ii) whose domain isn't equal to its image
iii) whose codomain isn't equal to its image
iv) a function $f$ from ...
user1071088
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Prove that $0 < g(x) - \ln x \leq \ln\left(\frac{x+2}{x}\right)$ for $x > 0$
$$g(x) = \ln(x + 1 + e^{-x})$$
My question is prove that $0 < g(x) - \ln x \leq \ln\left(\frac{x+2}{x}\right)$ for $x > 0$
How do I do that?
My attempts:
I have only successfully proved the ...
- 433
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If $f$ is a function such that $f(f(x))=x^{2}-1$ determine the function $f(f(f(f(x))))$
I have tried $f(f(f(f(x))))=f\left(f\left(x^{2}-1\right)\right)$ . Since we know that $f(f(x))=x^{2}-1$, we have
$$
\begin{aligned}
f\left(f\left(x^{2}-1\right)\right) &=\left(x^{2}-1\right)^{2}-1 ...
- 55
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Set of constant functions are uncountable.
Let $F=$ $\{$ $f: [0,1] \rightarrow \mathbb{R}$ $:$ $f$ is constant$ \} $. I must show that $F$ is uncountable.
Note, that for any $f \in F$, and any $c\in \mathbb{R}$, I will denote the constant ...
user643073