18. A function \( f \) is defined on the set of integers as follows \( f(x)=\left\{\begin{array}{ll}2 x+1 & \text { for }-1 \leq x<0 \\ -3 x+1 & \text { for } 0 \leq x<3 \\ -2 x-1 & \text { for } 3 \leq x<6\end{array}\right. \) Find the domain of \( f \). b. Find the range of \( f \). c. Is the function one-to-one?

1) \( (0,1)^{2 x}=10 \)

b. प्रमाणित गर्नुहोस् (Prove that): \( \frac{1}{1-\mathrm{x}^{\mathrm{a}-\mathrm{b}}}+\frac{1}{1-\mathrm{x}^{\mathrm{b}-\mathrm{a}}}=1 \)

Exercise 3.17 Determine if each one of the following system of linear equations has unique solution, no solution or infinitely many solutions. \( \begin{array}{ccc}x-y=1 & \text { b. } \begin{array}{c}x+y=1 \\ 2 x+3 y=4\end{array} & \begin{array}{c}x-2 y=1 \\ x+y=5\end{array} \\ \begin{array}{l}\text { a. } \\ x+4 y=2\end{array}\end{array} \)

a \( \frac{x^{3}-3 x^{2}+5}{x^{2}} \)

b. प्रमाणित गर्नुहोस (Prove that): \( \frac{1}{1-\mathrm{x}^{\mathrm{a}-\mathrm{b}}}+\frac{1}{1-\mathrm{x}^{\mathrm{b}-\mathrm{n}}}=1 \)