Express the function in the form
f ∘ g.
(Use non-identity functions for f and g.)
F(x) = (2x + x2)4
Express the function in the form
f ∘ g.
(Use non-identity functions for f and g.)
F(x) = (2x + x2)4
Express the function in the form f ∘ g. (Use non-identity functions for f and g.)
F(x) = (2x + x2)4
Assuming you meant:
F(x) = (2x + x^2)^4
g(x) = x + x^2
f(x) = x^4
check:
f ∘ g = f (g(x) )
= f(x+x^2)
= (x+x^2)^4
To express the function F(x) = (2x + x^2)^4 in the form f ∘ g, we need to decompose it into two separate functions. This can be done by introducing a new variable, let's say u, and breaking down F(x) into two parts: f(u) and g(x).
First, let's define g(x) = 2x + x^2. This function represents the inner operation that needs to be performed on x.
Next, let's define f(u) = u^4. In this case, u corresponds to g(x).
Now, to express F(x) in the form f ∘ g, we need to substitute g(x) into f(u). Thus, we have:
F(x) = f(g(x))
= f(2x + x^2)
= (2x + x^2)^4
Therefore, F(x) can be expressed in the form f ∘ g, where f(u) = u^4 and g(x) = 2x + x^2.