If the domain of f(x) is [-5,8], what is the domain of the function y = f(x+2) -1 ?
a) [-7,6]
b) [-3,9]
c) [-4,6]
d) [-7,7]
e) [-3,10]

i figured that the answer was d, however the answer key states that it is a. can you explain why?

The domain of function f(x) is [-5,8]. So no matter what the input to "f" is, the domain still applies. 
In this case the input is "x+2", set input equal to domain to solve for x.
These x values will represent new domain for f(x+2) -1.

x+2 = -5   >  x = -5 -2 = -7
x+2 = 8   > x = 8 -2 = 6

Therefore domain is [-7,6]

i = 2 / - 5

step-by-step explanation:

evaluation of ( 2 - 4 ) ( p + q ) when p = 2 and q = 5 i, by putting values of p and q,                                                                    

0 = ( 2 - 4 ) ( p + q )0 = ( 2 - 4 ) ( 2 + 5 i ),   by multiplying these0 = ( 4 + 10 i - 8 - 20 i )0 = 4 - 8 + 10 i - 20 i0 = - 4 -10 i   0 = 2 ( - 2 - 5 i )0 / 2 = - 2 - 5 i- 2 - 5 i = 0- 5 i = 2i = 2 / - 5