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Question Number 86030 by oustmuchiya@gmail.com last updated on 26/Mar/20

$$Tbefunction\mathbf{f}and\mathbf{g}aredefinedby\mathbf{f}\left(\mathbf{x}\right)=2\mathbf{x}-3and\mathbf{g}\left(\mathbf{x}\right)=3\mathbf{x}.$$$$\mathbf{F}ind\left(\mathbf{a}\right){\mathbf{f}}^{-1}\left(\mathbf{x}\right)\left(\mathbf{b}\right)\mathbf{gf}\left(\mathbf{x}\right)\left(\mathbf{c}\right)\mathbf{gf}\left(2\right)$$

Commented by Rio Michael last updated on 26/Mar/20

$$f:x\to 2x-3\mathrm{and}\mathrm{g}:x\to 3x$$$$\left(\mathrm{a}\right)\mathrm{let}y=f\left(x\right)\Rightarrow y=2x-3$$$$orx=2y-3\Rightarrow y=f^{-1}\left(x\right)=\frac{x+3}{2},x\in \mathbb{R}$$$$\left(\mathrm{b}\right)\mathrm{g}f\left(x\right)=\mathrm{g}\left[f\left(x\right)\right]=3(2x-3)=6x-9$$$$\left(\mathrm{c}\right)\mathrm{gf}\left(2\right)=6\left(2\right)-9=3$$

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