Home
Class 12
MATHS
Let RR^(+) be the set of positive real n...

Let `RR^(+)` be the set of positive real numbers and `f: RR rarr RR ^(+)` be defined by `f(x) =e^(x)` . Show that, f is bijective and hence find `f^(-1)(x)`

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1)(x) =log _(e)^(x)`
Promotional Banner

Topper's Solved these Questions

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|12 Videos
  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( very short answer type questions)|22 Videos
  • LOGARITHM

    CHHAYA PUBLICATION|Exercise Long Answer Type Question|12 Videos
  • MATHEMATICAL REASONING

    CHHAYA PUBLICATION|Exercise JEE Main (AIEEE) Archive (2016 )|1 Videos

Similar Questions

Explore conceptually related problems

Let RR be the set of real numbers and f: RR rarr RR be defined by , f(x) =x^(3) +1 , find f^(-1)(x)

Let RR be the set of real numbers and the mapping f: RR rarr RR be defined by f(x)=2x^(2) , then f^(-1) (32)=

Let RR be the set of real numbers and f : RR to RR be defined by f(x)=sin x, then the range of f(x) is-

Let RR be the set of real numbers and f:RR rarr RR be defined by , f(x)=2x^(2)-5x+6 .Find f^(-1)(5) and f^(-1)(2)

Let RR be the set of real number and f: RR rarr RR , be given by f(x)=2x^(2)-1 . .Is this mapping one -one ?

Let the function f: RR rarr RR be defined by, f(x)=x^(3)-6 , for all x in RR . Show that, f is bijective. Also find a formula that defines f ^(-1) (x) .

Let RR be the set of real numbers and f, Rrto RR be defined by f (x)= cos ec x(x ne npi, n in z): then image set of f is-

Let RR be the set of real numbers and f:RR rarr RR be defined by , f(x)=2x +1 . Find g: RR rarr RR , such that (g o f) (x) =10 x+10

Let A be the set of quadrilaterals in a plane and RR^(+) be the set of positive real numbers. Prove that, the function f: A rarr RR ^(+) defined by f(x) = area of quadrilateral x, is * many-one and onto.

Let RR be the set of all real numbers and f : R to R be given by f(x) = 3 x^(2) +1 then the set f^(-1) ([1,6]) is -