The composite function f(g(x)) is defined as sec(|x|) or 1/cos(|x|), where g(x) = |x| and f(x) = sec(x). The domain of this function is all real numbers except for the points where sec(x) is undefined, specifically at x = (2n+1)π/2 for n ∈ ℤ. The x-intercept occurs at f(g(0)) = sec(0) = 1, while the y-intercept is also at (0, 1). Asymptotes exist at the same points where sec(x) is undefined.
PREREQUISITESStudents studying calculus, particularly those focusing on composite functions and trigonometric analysis, as well as educators seeking to clarify these concepts in a teaching context.
Cuisine123 said:Homework Statement
Given g(x)=|x| and f(x)=secx
1)Determine an equation for (f(g(x))
2)State the domain
3)x and y intercepts
4)any asymptotes
Homework Equations
N/A
The Attempt at a Solution
f(g(x))=sec|x| or 1/cos|x|
"Equation" isn't the right word here. Do you mean formula? Why not just f(g(x))= f(|x|)= sec(|x|)?Cuisine123 said:Homework Statement
Given g(x)=|x| and f(x)=secx
1)Determine an equation for (f(g(x))
What is the domain of |x|? Which of those are in the domain of sec(x)?2)State the domain
What is f(g(0))? where is f(g(0))= 0?3)x and y intercepts
Are there any values of x for which sec(x) is not defined?4)any asymptotes
Good. Now continue.Homework Equations
N/A
The Attempt at a Solution
f(g(x))=sec|x| or 1/cos|x|