Express the function in the form f ∘ g. (Use non-identity functions for f and g.)
u(t) = cot(t)
{f(t), g(t)} =
Well, this is a math problem, but I guess I can clown around with it! How about we let f(t) = sin(t) and g(t) = arccot(t). That way, we can express u(t) = cot(t) as f(g(t)). So, f ∘ g = sin(arccot(t)). Ta-da!
To express the function u(t) = cot(t) in the form f ∘ g, we need to find non-identity functions f(t) and g(t).
Let's define f(t) = cot(t) and g(t) = t.
Now we can express the function u(t) as the composition of f and g: u(t) = f(g(t)).
Substituting the definitions of f(t) and g(t) into the expression, we get:
u(t) = cot(t) ∘ t
Therefore, u(t) = cot(t) ∘ t.
To express the function u(t) = cot(t) in the form f ∘ g, we need to find two non-identity functions f(t) and g(t) such that u(t) = f(g(t)).
Let's start by simplifying the function u(t) = cot(t). The cotangent function is the reciprocal of the tangent function, so we can express it as:
u(t) = 1 / tan(t)
To find f(t) and g(t), we can break down the cotangent function into two steps. Firstly, we can define a function g(t) that calculates the tangent of t:
g(t) = tan(t)
Secondly, we can define a function f(t) that takes the reciprocal of its input:
f(t) = 1 / t
Now, we can see that if we combine these two functions, we get:
f(g(t)) = 1 / (tan(t))
This expression is equivalent to u(t) = cot(t), which means that f(t) = 1 / t and g(t) = tan(t) satisfy the condition u(t) = f(g(t)).
Therefore, the function u(t) = cot(t) can be expressed as f ∘ g, where f(t) = 1 / t and g(t) = tan(t).