Answer:
f(g(x)) = sec(sin(x)) Third option
Step-by-step explanation:
In this problem we have 2 functions:
g(x) = sin(x)
f(x) = sec(x)
Where sec(x) = 1/cos(x)
Then we find f (g (x)) by introducing the function g into the function f.
The result is as follows:
f(g(x)) = sec(sin(x))
We know that the domain of the sec(x) are all values of x of the form [tex]x = \frac{k\pi}{2}[/tex] where k is an odd integer.
On the other hand the domain of sin(x) are all real numbers.
Then the domain of f(g(x)) must be all values of x such that sin(x) is different from [tex]x = \frac{k\pi}{2}[/tex]
Sin(x) is never equal to [tex]x = \frac{k\pi}{2}[/tex]. Therefore the domain of f(g(x)) are all real numbers, and its rank is [tex]1 \leq x\leq 1.85[/tex]
Where 1.85 is the maximum value that reaches when [tex]x = \frac{k\pi}{2}[/tex]
