Let f(x) = sin⁻¹(5 - 2x). Find the smallest and the largest x for which f(x) is defined…

Step 1. The condition. $-1 \le 5 - 2x \le 1$.

Step 2. Solve. Subtract $5$: $-6 \le -2x \le -4$. Divide by $-2$ and reverse the inequalities: $3 \ge x \ge 2$.

Step 3. The largest value. The inverse sine takes the value $\dfrac{\pi}{2} = 1.5708$ when its input is $1$. That happens at $5 - 2x = 1$, which is $x = 2$.