SOLUTION: f(x) = |x|
g(θ) = sin θ
f(g(x)) = f(sin θ)
f(g(x)) = |sin θ|
How do I find the domain?
g(f(x)) = g(|x|)
g(f(x)) = sin θ (|x|)
How do I find
Algebra ->
Trigonometry-basics
-> SOLUTION: f(x) = |x|
g(θ) = sin θ
f(g(x)) = f(sin θ)
f(g(x)) = |sin θ|
How do I find the domain?
g(f(x)) = g(|x|)
g(f(x)) = sin θ (|x|)
How do I find
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Question 784582: f(x) = |x|
g(θ) = sin θ
f(g(x)) = f(sin θ)
f(g(x)) = |sin θ|
How do I find the domain?
g(f(x)) = g(|x|)
g(f(x)) = sin θ (|x|)
How do I find the domain?
Just the same way you would find the domain in any composite function. First find any values that would cause the inner function to be undefined and exclude them. Then find any values that would cause the value of the inner function to be a value that would make the outer function undefined.
In your case, both of your functions have domains that are all real numbers, so no matter how you compose them, the composite function also has a domain that is all real numbers.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
