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Question Number 168428 by mnjuly1970 last updated on 10/Apr/22

$$$$$$solve$$$$f\left(x\right)=x+\sqrt{x^2-3x+2}$$$$R{}_f=?R_f:rangoff$$

Answered by MJS_new last updated on 11/Apr/22

$$f\left(x\right)\mathrm{is}\mathrm{defined}\mathrm{for}x⩽1\mathrm{oe}x⩾2$$$$\mathrm{for}-\mathrm{\infty }<x⩽1\mathrm{we}\mathrm{get}\frac{3}{2}>f\left(x\right)⩾1$$$$\mathrm{for}2⩽x<+\mathrm{\infty }\mathrm{we}\mathrm{get}2⩽f\left(x\right)<+\mathrm{\infty }$$$$\mathrm{the}\mathrm{range}\mathrm{is}[1;\frac{3}{2})\cup [2;+\mathrm{\infty })$$

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