Let ` f : N to N : f (x) =2x, g : N to N : g (y) = 3y+ 4`
and ` h : N to N : h (z) = ` sin z
Show that h o ( g o f) = (h o g ) o f .

Let f : R to R : f (x) = (2x -3) " and " g : R to R : g (x) =(1)/(2) (x+3) show that (f o g) = I_(R) = (g o f)

Let f : R to R : f (x) =x^(2) " and " g: R to R : g (x) = (x+1) Show that (g o f) ne (f o g)

Consider f" ":" "N ->N , g" ":" "N ->N and h" ":" "N ->R defined asf" "(x)" "=" "2x , g" "(y)" "=" "3y" "+" "4 and h" "(z)" "=" "s in" "z , AA x, y and z in N. Show that ho(gof ) = (hog) of.

Let f : R to R : f (x) =(2x +1) " and " g : R to R : g (x) =(x^(2) -2) Write down the formulae for (i) ( g o f) (ii) ( f o g) (iii) ( f o f) (iv) ( g o f)

(Associativity ) Let f: A to B , g : B to C " and " h: C to . Then prove that ( h o g) o f = h o ( g o f )

Let f : R to R : f (x) = x^(2) + 2 "and " g : R to R : g (x) = (x)/(x-1) , x ne 1 . Find f o g and g o f and hence find (f o g) (2) and ( g o f) (-3)

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z AZ, CX, FU, ….

Consider f g and h are real-valued functions defined on R. Let f(x)-f(-x)=0 for all x in R, g(x) + g(-x)=0 for all x in R and h (x) + h(-x)=0 for all x in R. Also, f(1) = 0,f(4) = 2, f(3) = 6, g(1)=1, g(2)=4, g(3)=5, and h(1)=2, h(3)=5, h(6) = 3 The value of f(g(h(1)))+g(h(f(-3)))+h(f(g(-1))) is equal to