Question

3

Answer 1

if \[|a| \le 1\]
then
\[ |3 + a^{3}| \le 4\]

Answer 2

Triangle inequality says \(|x+y|\leq|x|+|y|\)

So \(|3+a^3|\leq |3|+|a^3|\)

But \(|a|\leq 1\\|a|^3\leq 1\\|a^3|\leq 1\\|3|+|a^3|\leq|3|+1=4\)

Put all in \(|3+a^3|\leq|3|+|a^3|\leq 4\rightarrow |3+a^3|\leq 4~~q.e.d\)

Answer 3

Thank you