Explanation:
f(x) = x² + 5 g(x) = x + 4
for f(g(x)) or (f○g)(x) we take the expression of g and place it everywhere in the expression of f where x is mentioned.
so, (x + 4) goes into (x² + 5) giving us
((x + 4)² + 5) = x² + 8x + 16 + 5 = x² + 8x + 21
so, (2) is the correct answer.
8.
the same principle
f(x) = 2x + 9 g(x) = (x - 9)/2
just here we take f and put it into g :
g(f(x)) = ((2x + 9) - 9)/2 = 2x/2 = x
so,
(a) g(f(15)) = 15
(b) g(f(-3)) = -3
(c) g(f(x)) = x
to verify e.g. (a) we use x = 15 in f(x)
f(15) = 2×15 + 9 = 30 + 9 = 39
and then we use this result as new x = 39 in g :
g(39) = (39 - 9)/2 = 30/2 = 15
correct.