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Q:
$f\left(x\right)$ is a continuous and differentiable function defined in $[0,\infty)$. If $f\left(0\right)=1$ and $f'\left(x\right)>3f\left(x\right)\ $ $∀\ x\ \ge0$ then prove that $f\left(x\right)\ge e^{3x}\ ∀\ x\ \ge0$
Approach:
Given $$f'\left(x\right)>3f\left(x\right)\ $$
Let $f\left(x\...
I need to solve the following exercise.
Let $X$ be a non empty set and $P_2$ the set whose elements are all the subsets of $X$ that have $1$ or $2$ elements.
We have $f$ :
$f : X^2 \rightarrow P2$
$(x, y) \mapsto \{x, y\}$
Let $Y\in{P2}$. Determine $f^{-1}(\left\{{Y}\right\})$ and find its cardin...
