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Question Number 23785 by tawa tawa last updated on 06/Nov/17

$$\mathrm{A}\mathrm{function}\mathrm{f}\mathrm{is}\mathrm{define}\mathrm{by}\mathrm{f}:\to 3-2\mathrm{sinx},\mathrm{for}0⩽\mathrm{x}⩽360$$$$\mathrm{find}\mathrm{the}\mathrm{range}\mathrm{of}\mathrm{f}$$

Answered by mrW1 last updated on 06/Nov/17

$$\sin x\in [-1,+1]$$$$f=3-2\sin x\in [1,5]$$

Commented by tawa tawa last updated on 06/Nov/17

$$\mathrm{How}\mathrm{please},\mathrm{explain}\mathrm{more}.$$

Commented by Joel577 last updated on 06/Nov/17

$$\mathrm{The}\mathrm{range}\mathrm{of}\mathrm{function}\sin x\mathrm{is}[-1,1]$$$$\mathrm{Hence}\mathrm{the}\mathrm{minimum}\mathrm{value}\mathrm{of}f\left(x\right)=3-2\sin x$$$$\mathrm{is}1\mathrm{and}\mathrm{the}\max \mathrm{is}5$$

Commented by tawa tawa last updated on 06/Nov/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{But}\mathrm{i}\mathrm{have}\mathrm{not}\mathrm{really}\mathrm{understand}.$$

Commented by mrW1 last updated on 06/Nov/17

$$f\left(x\right)=3-2\sin xisminimumif\sin x=1,$$$$andtheminimumis3-2=1.$$$$$$$$f\left(x\right)=3-2\sin xismaximumif\sin x=-1,$$$$andthemaximumis3+2=5.$$$$$$$$\Rightarrow 1⩽f\left(x\right)⩽5$$

Commented by tawa tawa last updated on 06/Nov/17

$$\mathrm{Wow},\mathrm{now}\mathrm{i}\mathrm{understand}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Answered by FilupES last updated on 09/Nov/17

$$f\left(x\right)=3-2\sin \left(x\right),0⩽x⩽360$$$$-1⩽\sin \left(x\right)⩽1,\mathrm{\forall }x$$$$$$$$g=2\sin \left(x\right)$$$$\min \left(g\right)=-2$$$$\max \left(g\right)=2$$$$$$$$f\left(x\right)=3-g$$$$\min \left(f\right)=3-\max \left(g\right)=1$$$$\max \left(f\right)=3-\min \left(g\right)=5$$$$$$$$\therefore 1⩽f\left(x\right)⩽5$$

Commented by tawa tawa last updated on 11/Nov/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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