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Find the domain of f(x) = ln(tanx) on the interval [-π,π]. a. all x in [-π/2, π/2]...

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vass3 | (Level 2) eNoter

Posted August 3, 2013 at 9:03 PM via web

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Find the domain of f(x) = ln(tanx) on the interval [-π,π].

a. all x in [-π/2, π/2]

b. all x in (-π, -π/2) and (0, π/2)

c. all x in (0, π/2)

d. all x in (0,π)

e. all x in (-π, π)

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aruv | High School Teacher | (Level 2) Valedictorian

Posted August 4, 2013 at 3:15 AM (Answer #1)

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`f(x)=g(h(x))`

`g(x)=ln(x)`

`h(x)=tan(x)`

domain of g(x)=`[-pi,pi]`

codomain of g(x)=`(-oo,oo)`

codmain of g(x)= domain of h(x)

since ln is defied for positive real numbers only .

Thus domain of g(x) is `(-pi,-pi/2)uu(0,pi/2)`

Thus domain of f(x) is same as domain of g(x).

So domain of f(x) is `(-pi,-pi/2)uu(0,pi/2)`

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