Practice Problems: Let \( \mathrm{A}=\{-2,-1,0,1,2 \quad\} \). Define a relation R from A to A by \( \mathrm{x} R \mathrm{y} \) if and only if 3 does divides \( \mathrm{x}-\mathrm{y} \) for any \( \mathrm{x}, \mathrm{y} \in \mathrm{A} \). a. List down the elements of R . b. Find the domain of R c. Find the range of R d. Create an arrow diagram of R Let \( \mathrm{A}=\{0,1,2,3,4,5\} \). Define a relation R from A to A by \( x R y \) if and only if \( \mathrm{x}+\mathrm{y}<4 \) for any \( \mathrm{x}, \mathrm{y} \in \mathrm{A} \). a. List down the elements of R . b. Find the domain of R c. Find the range of R d. Create an arrow diagram of R 3. If \( \left.f(x)=2 x^{2}+5, g(x)=\sqrt{( } 3 x+1\right) \) and \( h(x)=3 x^{2}+2 x \). Evaluate the following: a. \( (\mathrm{f} \cdot(\mathrm{g} \cdot \mathrm{h})(\mathrm{x}) \) b. \( (\mathrm{go}(\mathrm{goh}))(\mathrm{x}) \) c. \( ((\mathrm{goh})+\mathrm{h})(\mathrm{x}) \)
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