In order to answer the question we need to focus on the value we're being asked about:
If -2≤x≤2, then the part of the function we should consider is
[tex]2x-5.[/tex]
If 2[tex]x^3-2.[/tex](a) We need to find f(0). Since 0 is bewteen -2 and 2, we're considering the first part of the function. Then
[tex]f(0)=2(0)-5=0-5=-5.[/tex]
(b) Now we want to find f(1). Once again, since 1 is between -2 and 2, we're considering the first part of the function, so
[tex]f(1)=2(1)-5=2-5=-3.[/tex]
(c) This time, we want to find f(2). Since 2≤2, we are still considering the first part of the function, so we need to consider
[tex]f(2)=2(2)-5=4-5=-1.[/tex]
(d) Finally, we want to find f(5). 5 is greater than 2, but 5≤5, so we need to consider the second part of the function this time. Let's do so:
[tex]f(5)=5^3-2=25\cdot5-2=125-2=123.[/tex]
