Home
Class 12
MATHS
Consider f: R->Rgiven by f(x) = 4x + 3. ...

Consider `f: R->R`given by `f(x) = 4x + 3`. Show that f is invertible. Find the inverse of f.

Text Solution

Verified by Experts

The correct Answer is:
`f ^(-1) ` is given by `f ^(-1) (y ) = (y -3)/(4)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.4|13 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise MISCLELLANEOUS EXERCISE ON CHAPTER 1|19 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

Consider f : R rarr R given by f(x) = 4x +3. Show that f is invertible. Find inverse of f .

Let Y = {n^(2) :n in N} subN Consider f: N rarr Y as f(n) = n^2 . Show that f is invertible. Find the inverse of f.

Consider f: R ^+ to [4 ,oo] given by f(x) =x^2 + 4 show that f is f invertible with the inverse f^(-1) of given by f^(-1) (y) = sqrt(y-4) where R^+ is set of all non - negative real numbers .

Consider f: R ^+ to [4 ,oo] given by f(x) =x^2 + 4 show that f is f invertible with the inverse f^(-1) of given by f^(-1) (y) = sqrt(y-4) where R^+ is set of all non - negative real numbers .

Consider f : R_(+) rarr [-5,oo) given by f(x) = 9x^(2) +6x-5 . Show that f is invertible with f^(-1)(y) = ((sqrt(y+6)-1)/3)

f: N rarr R , f(x) = 4x^(2) +12x +5 . Show that f: N rarr R is invertible function . Find the inverse of f.

Consider f, R^(+ ) to [-5 , oo) given by f(x) = 9x^(2) + 6x-5 . Show that f is invertible with f^(-1) (y) =(((sqrt( y+6)) - 1)/( 3)) , where R^(+) is the set of all non-negative real numbers.

Let f:N rarr Y be a function defined as f(x) = 4x + 3, where, Y = { y in N:y = 4x + 3 for some x in N }. Show that f is invertible. Find the inverse.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.