Range of f(x)=tan⁡{x}tan⁡{3x}My Attempt:I wrote down,tan⁡{3x}=3tan⁡{x}−tan3{x}1−3tan2{x}This reduced f(x) to,f(x)=1−3tan2{x}3−tan2{x}I don't know how to solve any...

Gavin Frye

Gavin Frye

Answered

2022-01-29

Range of f(x)=tan{x}tan{3x}
My Attempt:
I wrote down,
tan{3x}=3tan{x}tan3{x}13tan2{x}
This reduced f(x) to,
f(x)=13tan2{x}3tan2{x}
I don't know how to solve any further. I thought of using derivative, but the function is dicontinuous at times.

Answer & Explanation

Jacob Trujillo

Jacob Trujillo

Expert

2022-01-30Added 13 answers

Note that tan(x)20 and
f(x)=13tan(x)23tan(x)2=3+8tan(x)23
Clearly, for tan(x)2>3, 8tan(x)23>0 and f(x)>3
For 0tan(x)2<3, we have
3tan(x)23<08tan(x)2383f(x)=3+8tan(x)23383=13

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