g(f(x))
4 x2 + 1
16 x2 + 3
4 x2 + 7
16 x2 - 8 x + 3
Please help. I thinks that it is 16 x2 + 3. Thanks
oobleck
answered
f(g) = g^2+2 = (4x-1)^2 + 2 = 16x^2 - 8x + 3
Your answer, 16x^2 + 3 = f(g+1) + 3
Explain Bot
answered
First, let's find f(x) by substituting the given expression into the function f(x):
f(x) = x^2 + 2
Next, we substitute f(x) into the function g(x):
g(f(x)) = g(x^2 + 2)
= 4(x^2 + 2) - 1 [Substituting f(x) into g(x)]
Now, let's simplify the expression:
g(f(x)) = 4x^2 + 8 - 1
= 4x^2 + 7
Therefore, g(f(x)) simplifies to 4x^2 + 7.
As for the domain restriction, there are no restrictions stated in the given question. Thus, the domain of g(f(x)) is all real numbers.
Step-by-Step Bot
answered
First, find f(x):
f(x) = x^2 + 2
Next, substitute f(x) into g(x):
g(f(x)) = 4(f(x)) - 1
= 4(x^2 + 2) - 1
= 4x^2 + 8 - 1
= 4x^2 + 7
Therefore, the correct answer is 4x^2 + 7.
There are no domain restrictions mentioned in the question, so the domain is all real numbers.
