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"let f(x)=√(1-x),g(x)=x/(x2-1) find fog and domin (f),domain (g) and domain (fog)"
f(x)= 5/(x2-1) and g(x)=√(x+7) find fog and domain (fog)
find the period of the function ...f(x)= tan((x/3)-π)
The function f(x)=tan(x/3-π) has period of 9π, & here's why :
Let's ask our selves when tang(α)=∞ ? it happens when α=π/2,
so { -π/2 ≤ x/3-π ≤ π/2 } -> { π/2 ≤ x/3 ≤ 3π/2 } ->
{ 3π/2 ≤ x ≤ 9π/2 } -> Period=(9π-3π)/2=3π. That means :
tan[Ø/3-π]=tan[(Ø+3π)/3-π].
f(x)=√(1-x) , g(x)=x/(x^2-1)
---------------------------
Domain{f}: 1-x ≥ 0 -> x ≥ 1
Domain{g}: All x
fog=g(f)=f/(f^2-1)=√(1-x)/(1-x-1)=-√(1-x)/x
gof=f(g)=√(1-g)=√[1-x/(x^2-1)]
Domain{fog}: 1-x ≥ 0 -> x ≥ 1
Domain{gof}: 1-x/(x^2-1) ≥ 0 -> (x^2-1)^2 ≥ x(x^2-1) -> x ≥ -1 .
As for f(x)= 5/(x2-1) and g(x)=√(x+7) , I will leave it for you as
an exercise .... Any problem, I'm here.
Alon
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Alon Mandes
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