Is this set a subspace of $\Bbb{R}^{[4, 6]}$

Question

I am confused as to what this notation means?

$$\textsf W = \{f \in \Bbb{R}^{[4, 6]} : (\forall x \in [4,6])(|f(x)| \le 1)\}$$

Answer 1

You're looking at the set of all function $f:[4,6]\to \mathbb{R}$. Such that $|f(x)|\le 1$ for every $x\in [4,6]$. Is this set closed under scalar multiplication?

Answer 2

$\mathbb{R}^{[4,6]}$ is the set of all functions $f$ that going from $[4,6]$ to $\mathbb R$. Hence, $\textsf W$ consist of all those functions $f\in\mathbb{R}^{[4,6]}$ for which $|f(x)|\leq 1$ for all $x\in[4,6]$ (because $[4,6]$ is the domain of this functions).

Answer 3

The constant function 1 belongs to your set. Its double not. Hence it is not a vector subspace.