Find (f◦g)(x) and (g◦f)(x).
f(x)=4x(squared)+3; g(x)=4x−2(f◦g)(x)=______(Simplify your answer.)
I keep getting lost on these f(x) and g(x)problems
(f◦g) = f(g) = 4g^2+3 = 4(4x-2)^2+3
(g◦f) = g(f) = 4f-2 = 4(4x^2+3)-2
now just simplify
sometimes it helps not to include all those (x)'s
(f◦g)(x) = f(g(x)) = f(4x-2) = 4(4x-2)^2+3
you can replace g first or evaluate f(g) and then plug in g
To find (f◦g)(x), we need to substitute the function g(x) into the function f(x).
Given f(x) = 4x^2 + 3 and g(x) = 4x - 2, we substitute g(x) into f(x) by replacing x in f(x) with g(x).
So, (f◦g)(x) = f(g(x)) = f(4x - 2).
To find (f◦g)(x), we need to substitute 4x - 2 into the function f(x).
(f◦g)(x) = f(4x - 2) = 4(4x - 2)^2 + 3.
Now, let's simplify this expression to get the answer.
To simplify, we need to apply the order of operations (PEMDAS/BODMAS) and expand the squared term.
(f◦g)(x) = 4(16x^2 - 16x + 4) + 3
= 64x^2 - 64x + 16 + 3
= 64x^2 - 64x + 19.
So, (f◦g)(x) = 64x^2 - 64x + 19.
Now let's find (g◦f)(x) by substituting f(x) into g(x).
(g◦f)(x) = g(f(x)) = g(4x^2 + 3).
Substituting 4x^2 + 3 into the function g(x), we get:
(g◦f)(x) = g(4x^2 + 3) = 4(4x^2 + 3) - 2.
(g◦f)(x) = 16x^2 + 12 - 2
= 16x^2 + 10.
So, (g◦f)(x) = 16x^2 + 10.