Home
Class 12
MATHS
Consider f: Rrarr[-5, oo] given by f(x)...

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

Text Solution

Verified by Experts

The correct Answer is:
`(-1+sqrt(x+6))/3`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION I) (MULTIPLE CHOICE QUESTIONS)|11 Videos
  • RELATIONS AND FUNCTIONS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION II) (SHORT ANSWER TYPE QUESTIONS)|6 Videos
  • RELATIONS AND FUNCTIONS

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (SECTION IV) |7 Videos
  • PROBABILITY

    BETTER CHOICE PUBLICATION|Exercise Previous year Board.s questions for practice|43 Videos
  • THREE DIMENSIONAL GEOMETRY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE |60 Videos

Similar Questions

Explore conceptually related problems

Consider f: Rrarr [- 5, ∞) given by f(x) = 9x^2 + 6x- 5 . Show that f is invertible. Find the inverse of f.

Consider f : R_+ rarr (-9, infty) given by f(x) = 5x^2 + 6x - 9 . Prove that f is invertible with f^-1 (y) = (sqrt(54+5y)-3)/(5)

Consider f:R^(+) rarr [-5, oo] given by f (x) = 9x^(2) + 6x - 5 show that 'f' is invertible. Find the inverse of f .

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

Consider rrarr[4,infty] given by f(x)=x^2+4 . Show that f is invertible with the increase f^-1 of f given by f^-1(y)=sqrt(y-4) , where R is the set of all non-negative real numbers.

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