Home
Class 12
MATHS
Consider f: {1,2,3} to {a,b,c} and g: {a...

Consider `f: {1,2,3} to {a,b,c} and g: {a,b,c} to `{apple, ball, cat} defined as `f (1) =a, f (2) =b, f (3)=c, g (a)` = apple,` g (b) = ` ball and g (c )= cat. Show that f, g and gof are invertible. Find out `f ^(-1) , g ^(-1) and ("gof")^(-1)` and show that `("gof") ^(-1) =f ^(-1) og ^(-1).`

Text Solution

Verified by Experts

The correct Answer is:
`I _(z)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f: {2,3,4,5}to {3,4,5,9}and g: {3,4,5,9}to {7,11,15} be function defined as f (2) =3, f (3) = 4, f (4) f (5)=5 and g (3) =g (4)=7 and g (5) =g (9) =11. Find gof.

Consider f: {1,2,3} to {a,b,c} given by f (1) =a , f (2) =b and f (3)=c. Find f ^(-1) and show that (f ^(-1)) ^(-1) =f.

Find the gof and fog if f(x) = 8x^(3)" and "g(x)=x^(1/3)

If f:RrarrR defined by f(x)=(4x+3) , show that f is invertible and find f^(-1 .

If f: R to R and g: R to R are given by f(x)= cosx and g(x) =3x^(2) .Show that gof ne fog

Show that if f: A to B and g : B to C are onto, then gof A to C is also onto.

Show that if f: A to B and g: B to C are onto, then gof : A to C is also onto.

Let f:{1,2,3} to {a,b,c} be one-one and onto function given by f (1) =a, f (2) =b and f (3) =c. Show that there exists a function g : {a,b,c} to {1,2,3} such that gof =I _(x) and fog =I _(y), where, X = {1,2,3} and Y={a,b,c}.

If f(a) = 2 , f ' (a) = 1 , g (a) = -1 , g'(a) = 2 , then lim_(x to a) (g (x) * f (a) - g (a) * f(x))/( x- a) is equal to