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Question Number 106707 by bemath last updated on 06/Aug/20

$$@\mathrm{bemath}@$$$$\mathcal{G}\mathrm{iven}\{\begin{array}{l}\mathrm{f}\left(\mathrm{x}\right)=2\mathrm{x}+3\\ (\mathrm{g}\circ \mathrm{f})\left(\mathrm{x}\right)=2\mathrm{x}-1\end{array}$$$$\mathrm{find}(\mathrm{f}\circ \mathrm{g})\left(2\right).$$

Answered by john santu last updated on 06/Aug/20

Answered by mathmax by abdo last updated on 06/Aug/20

$$\mathrm{f}\left(\mathrm{x}\right)=2\mathrm{x}+3\mathrm{and}\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=2\mathrm{x}-1\Rightarrow \mathrm{g}(2\mathrm{x}+3)=2\mathrm{x}-1$$$$\mathrm{let}2\mathrm{x}+3=\mathrm{t}\Rightarrow \mathrm{x}=\frac{\mathrm{t}-3}{2}\Rightarrow \mathrm{g}\left(\mathrm{t}\right)=2\left(\frac{\mathrm{t}-3}{2}\right)-1=\mathrm{t}-4$$$$\mathrm{g}\left(\mathrm{t}\right)=\mathrm{t}-4\Rightarrow \mathrm{fog}\left(2\right)=\mathrm{f}\left(\mathrm{g}\left(2\right)\right)=\mathrm{f}(-2)=-4+3=-1\Rightarrow$$$$\mathrm{fog}\left(2\right)=-1$$

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