Given that f (x) = x2+3x+6 and g (x) = x-3/2, solve for f (g (x)) when x=1

They want you to find the composite function and they evaluate it at a give value for x ... first the composite function ...

f (g (x)) = (x-1.5) ^2+3 (x-1.5) + 6

f (g (x)) = x^2-3x+2.25+3x-4.5+6

f (g (x)) = x^2+3.75, this is the completed composition function ... now:

f (g (1) = 1+3.75=4.75