MATHS HOLIDAY HOMEWORK:- Relations and Functions

1-mark

Q.1.  If f(x)=x+7 and g(x)=x-7, then find fog(7)

Q.2.  Write fog if f:R->R and g:R->R, defind by f(x)=8x³ and      g(x)=x1/3

Q.3.   If * is a Binary Operation on the set Z on integers defined by a*b=a+b-5, then write the identity element of * on Z

2-MARK

Q.4.  Let * be any Binary Operation on Z defined by a*b=(3ab)/5, Show that * is commutative as well as associative. Also find the identity if it exists.

Q.5.  Consider f : [0,π/2]->R defined by f(x)=sinx and g : [0,π/2]->R and g(x)=cos x, Show that f and g are one-one, but f+g is not one-one

Q.6.  Find fog and gof if 

          i) f(x)=[x], and g(x)=sinx

         ii) f(x)=x²+2 and g(x)=1-(1/(1-x))

The last question is not clear, I will sent it to later

The next chapter's holiday homework will posted by me in a day or two. Try to complete this before them.