12. Let A={9,10,11,12,13} and let f : A (rightarrow) N be defined by f(n)=the highest prime factor of n. Find the range of f. Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation…
11. Let f be the subset of Z×Z defined by f={(ab,a+b) : a, b(in) Z}. Is f a function from Z to Z? Justify your answer. Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1.…
10. Let A={1,2,3,4}, B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11)} Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B.Justify your answer in each case. Relations and Functions Miscellaneous Exercise Previous Next…
9. Let R be a relation from N to N defined by R={((a,b) : a, bin N) and (a=b^2)}. Are the following true?(i) ((a,a) in R), for all (ain N)(ii) ((a,b) in R), implies ((b,a) in R)(iii) ((a,b) in R,…
8. Let f={(1,1),(2,3),(0,–1),(–1,–3)} be a function from Z to Z defined by (f(x)=ax+b), for some integers a, b. Determine a, b. Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined…
7. Let (f, g : Rrightarrow R ) be defined, respectively by f(x)=x+1, g(x)=2x–3. Find f+g, f–g and (frac{f}{g}). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{…
6. Let (f=left{left(x,frac{x^2}{1+x^2}right):mathrm{ x} in Rright}) be a function from R into R. Determine the range of f. Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0}…
5. Find the domain and the range of the real function f defined by (f(x)=left|x-1right|). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le…
4. Find the domain and the range of the real function f defined by (fleft(xright)=sqrt{x-1}). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le…
3. Find the domain of the function (fleft(xright)=frac{x^2+2x+1}{x^2-8x+12}). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le xlemathrm{10}\end{matrix}) (g(x)={begin{matrix}x^2,mathrm{ 0} le xle2\3x,mathrm{ 2}le xlemathrm{10}\end{matrix})…
