Category class 11

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})…

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}) Show that f is a function and g is not a function. Relations and Functions Miscellaneous Exercise Previous Next Class 11…

2. If (f(x)=x^2), find (frac{f(1.1)-f(1)}{(1.1-1)}). 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 xlemathrm{10}\end{matrix}) (g(x)={begin{matrix}x^2,mathrm{ 0} le xle2\3x,mathrm{ 2}le xlemathrm{10}\end{matrix}) Show that f…