Given the functions, f(x) = x2 + 2 and g(x) = 4x - 1, perform the indicated operation. When applicable, state the domain restriction.
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
To find the composition of two functions, we substitute the inner function f(x) into the outer function g(x) and simplify the expression.
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.
To find the composition g(f(x)), we need to substitute the function f(x) into the function g(x).
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.
g(f) = 4f-1 = 4(x^2+2) - 1 = 4x2 + 7
f(g) = g^2+2 = (4x-1)^2 + 2 = 16x^2 - 8x + 3
Your answer, 16x^2 + 3 = f(g+1) + 3