Express the function in the form f o g if g(t)=csc t
u(t)= sqrt(csc t)
f(t)=?
u(t) = √(g(t))
So, if f(t) = √t,
u(t) = f(g(t)) = (fog)(t)
To express the function u(t) = sqrt(csc(t)) in the form f o g, where g(t) = csc(t), we can substitute u(t) into f(t) as follows:
f(t) = u(g(t)) = sqrt(csc(g(t)))
Since g(t) = csc(t), we can substitute csc(t) into g(t) and simplify:
f(t) = sqrt(csc(csc(t)))
Therefore, f(t) = sqrt(csc(csc(t))).
To express the function in the form f o g, we need to substitute g(t) into u(t) and find the composition of the two functions.
Given:
g(t) = csc(t)
u(t) = sqrt(csc(t))
To find f(t), we substitute g(t) into u(t) as follows:
f(t) = u(g(t))
Replacing g(t) in u(t):
f(t) = sqrt(csc(g(t)))
Now, we substitute g(t) back in:
f(t) = sqrt(csc(csc(t)))
Therefore, the expression of the function f(t) = sqrt(csc(csc(t))).