Home
Class 12
MATHS
Verify whether the function f : N to Y d...

Verify whether the function `f : N to Y` defined by `f(x) = 4x + 3`, where `Y = {y : y = 4x + 3, x in N}` is invertible or not. Write the inverse of f(x) if exists.

Text Solution

Verified by Experts

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

Similar Questions

Explore conceptually related problems

Prove that the function f: N to Y defined by f(x) = x^(2) , where y = {y : y = x^(2) , x in N} is invertible. Also write the inverse of f(x).

Prove that the function f:N to Y defined by f(x) = 4x +3 , where Y=[y:y =4x +3,x in N] is invertible . Also write inverse of f(x).

Prove that the function f : R to R defined by f(x) = 3 - 4x , AA x in R is bijective.

Let f:NtoY be a function defined as f(x)=4x+3 , where Y={yinN,y=4x+3 for some x inN }. Show that f is invertible and its inverse is :

Prove that the function f: R to R defined by f(x) = 4x + 3 is invertible and find the inverse of 'f' .

Show that the function f : N to N defined by f(x) = x^(3), AA x in N is injective but not surjective.

Let f : N to R be defined by f(x) = 4x^(2) + 12x + 15 , show that f: N to S , where S is the function, is invertible. Also find the inverse.

If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

Show that the function f : N to N defined by f(x) = x^(2), AA x in N is injective but not surjective.

Let f: N to R be defined by f(x) = 4x^(2) + 12x+ 15 . Show that f: N to S where S is the range of function f, is invertible. Also find the inverse of f.