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Question Number 86129 by oustmuchiya@gmail.com last updated on 27/Mar/20

$$Giventhat\mathbf{f}\left(\mathbf{x}\right)=8\mathbf{x}and\mathbf{g}\left(\mathbf{x}\right)=\frac{3\mathbf{x}-2}{4},find$$$$\left(\mathrm{a}\right){\mathbf{f}}^{-1}\left(\mathbf{x}\right)\left(\mathrm{b}\right)anexpressionfor\mathit{f}\mathit{g}\left(\mathbf{x}\right)$$$$\left(\mathrm{c}\right)valueof\mathbf{x}which\mathbf{fg}\left(\mathbf{x}\right)=20$$

Commented by jagoll last updated on 27/Mar/20

$$\mathrm{a}){\mathrm{f}}^{-1}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{8}$$$$\mathrm{b})\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)=8\left(\frac{3\mathrm{x}-2}{4}\right)=6\mathrm{x}-4$$$$\mathrm{c})\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)=6\mathrm{x}-4=20$$$$\mathrm{x}=\frac{24}{6}=4$$

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