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?

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

\( f(x)=\frac{x+k}{x-1} \) and \( (5,2) \in f^{-1} \), then \( K= \)

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

6. Simplify these expressions and find then values if \( x=3, p=-1,4=-2 \) (i) \( 3 p+4+2 q+1 \) (ii) \( 8-6 x+4 x+3 \)

Solve the exponential equation: \( 3^{2x} = 81 \)