d) Are the follawing functions ore-to-one, onto or bjjection? (i)f(x)=2x+1(ii)f(x)=x2+7(iii)f(x)=(x+1)/(x+2)(iv)f(x)=x3(v)f(x)=x1​+ex2. Letnis a constant positive integer. Define a relationR∈Z×Zby \[ (x, y) \in R \Leftrightarrow(n \mid x-y \Leftrightarrow \exists k \in z, x-y=k n) \text {. } \] Prove thatRis an equivalence relation onz3. Rrove thatS3​is a group. 4. Find the solution of the requrrence relation \[ a_{n}=7 a_{n-1}-16 a_{n-2}+12 a_{n-3}+n 4^{n} \] witha0​=−2,a1​=0, anda2​=5. Show your work step-by-step.  Please give proper explanation and typed answer only.

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