Express the function in the form
f ∘ g. (Use non-identity functions for f and g.)
u(t) = tan(t)/ 4 + tan(t)
To express the function u(t) in the form f ∘ g, we need to find two non-identity functions, f and g, such that u(t) can be written as f(g(t)).
Let's start by considering the function g(t). We can choose g(t) = tan(t).
Now, let's find the function f that we can compose with g(t). We want to find f(g(t)) = u(t).
Given that u(t) = tan(t)/4 + tan(t), we can see that the second term tan(t) is added to the first term tan(t)/4.
Therefore, we can express u(t) in the form f ∘ g as follows:
f(g(t)) = (1/4)g(t) + g(t)
Replacing g(t) with tan(t), we have:
f(tan(t)) = (1/4)tan(t) + tan(t)
So, the function u(t) can be expressed in the form f ∘ g as:
u(t) = (1/4)tan(t) + tan(t)
To express the function u(t) in the form f ∘ g, we need to find two non-identity functions, f and g, such that u(t) = f(g(t)).
Let's start by defining f and g as follows:
g(t) = tan(t)
f(x) = x/4 + x
Now, we can substitute g(t) into f(x) to get:
u(t) = f(g(t)) = g(t)/4 + g(t)
Substituting g(t) = tan(t) back into the equation, we have:
u(t) = tan(t)/4 + tan(t)
So, u(t) can be expressed in the form f ∘ g as u(t) = f(g(t)) with f(x) = x/4 + x and g(t) = tan(t).
g(t) = tan(t)
f(t) = t/(4+t)
(f ∘ g)(t) = f(g) = g/(4+g) = tan(t)/(4+tan(t))