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Question Number 151460 by mathdanisur last updated on 21/Aug/21

$$\mathrm{if}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2-2\mathrm{x}+2$$$$\mathrm{and}\mathrm{g}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}}+1$$$$\mathrm{find}\left[\mathrm{f}o\mathrm{g}\right]\left(\mathrm{x}\right)=?$$

Answered by puissant last updated on 21/Aug/21

$$f\left(x\right)=x^2-2x+2;g\left(x\right)=\sqrt{x}+1$$$$\left[fog\right]\left(x\right)=f\left(g\left(x\right)\right)$$$$={(\sqrt{x}+1)}^2-2(\sqrt{x}+1)+2$$$$=x+2\sqrt{x}+1-2\sqrt{x}-2+2$$$$\left[fog\right]\left(x\right)=x+1..$$

Commented by mathdanisur last updated on 21/Aug/21

$$\mathrm{Thank}\mathrm{you}\mathbf{S}\mathrm{er}$$

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