Answer:
4x² + 4x + 1
Step-by-step explanation:
To obtain f(g(x)), substitute x = g(x) into f(x)
f(g(x)) = f(2x + 1) = (2x + 1)² = 4x² + 4x + 1
For this case we have by definition that:
[tex](f_ {0} g) (x) = f [g (x)][/tex]
They tell us that:
[tex]f (x) = x ^ 2\\g (x) = 2x + 1[/tex]
So:
[tex](f_ {0} g) (x) = f [2x + 1] = (2x + 1) ^ 2 = (2x) ^ 2 + 2 (2x) (1) + 1 ^ 2 = 4x ^ 2 + 4x + 1[/tex]
ANswer:
[tex]f [g (x)] = 4x ^ 2 + 4x + 1[/tex]
