Home
Class 12
MATHS
If R, is the set of all non-negative re...

If R, is the set of all non-negative real numbers prove that the `f : R, to [-5, oo)` defined by `f(x) = 9x^(2) + 6x - 5` is invertible. Write also `f^(-1)(x)`.

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1) = g(y) = (sqrt(y - 6)-1)/(3)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (One mark questions)|5 Videos
  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (Two marks questions)|5 Videos
  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise THREE MARKS QUESTIONS WITH ANSWERS|16 Videos
  • PUC SUPPLEMENTARY EXAMINATION QUESTION PAPER JUNE 2019

    SUBHASH PUBLICATION|Exercise PART E|4 Videos
  • SUPER MODEL QUESTION PAPER FOR PRACTICE

    SUBHASH PUBLICATION|Exercise PART - E|4 Videos

Similar Questions

Explore conceptually related problems

If R_(+) is the set of all non-negative real numbers prove that the f:R_(+) to (-5, infty) defined by f(x)=9x^(2)+6x-5 is invertible. 39. Write also, f^(-1)(x) .

If R, is the set of all non - negative real numbers prove that the function f:R_(+) to [-5, infty]" defined by "f(x)=9x^(2)+6x-5 is invertible. Write also f^(-1)(x) .

Let R+ be the set of all non-negative real number. Show that the faction f : R, to [4, oo) defined f(x) = x^(2) + 4 is invertible. Also write the inverse of f.

Let R_(+) be the set of all non-negative real numbers. Show that the function f: R_(+) to [4,oo] defind by f(x) = x^(2)+4 Is invertible and write the inverse of f.

Let f: R to R be defined by f(x) = x^(4) , then

Let R+ be the set of all non-negative real numbers. Show that the function f : R+ rarr [ 4 ,oo ] given by f(x) = x^(2) + 4 is invertible and write the inverse of f.

Prove that the function f : R to R defined by f(x) = 2x , AA x in R is bijective.

Let f : R to R be defined by f(x)=x^(4) , then

Let R+ be the set of all non negative real numbers. Show that the function f: R_(+) to [4, infty] given by f(x) = x^2 + 4 is invertible and write inverse of 'f'.