English

Let F : R+ → R, Where R+ Is the Set of All Positive Real Numbers, Such That F(X) = Loge X. Determine(A) the Image Set of the Domain Of F - Mathematics

Advertisements
Advertisements

Question

Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(a) the image set of the domain of f

Solution

Given:
f : R+ → R
and (x) = logex .............(i)

(a) f : R+ → R
Thus, the image set of the domain f = .

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Functions - Exercise 3.1 [Page 7]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 3 Functions
Exercise 3.1 | Q 7.1 | Page 7

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.

(b) f2 = {(1, 1), (2, 7), (3, 5)}


If fgh are real functions given by f(x) = x2g(x) = tan x and h(x) = loge x, then write the value of (hogof)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .

 


Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.


If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to


If  \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and}  g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to

 


If  \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,

 

If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\]  x ∈ R, then

 

The domain of definition of the function f(x) = log |x| is


The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is


The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is

 

Let  \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?

 


If f(m) = m2 − 3m + 1, find f(− x)


Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`


Check the injectivity and surjectivity of the following function.

f : N → N given by f(x) = x2 


Show that if f : A → B and g : B → C are one-one, then g ° f is also one-one


Express the following exponential equation in logarithmic form

e2 = 7.3890


Prove that alogcb = blogca


Solve for x.

2 log10 x = `1 + log_10 (x + 11/10)`


Answer the following:

Identify the following relation is the function? If it is a function determine its domain and range.

{(0, 0), (1, 1), (1, –1), (4, 2), (4, –2), (9, 3), (9, –3), (16, 4), (16, –4)}


Answer the following:

Find whether the following function is one-one

f : R → R defined by f(x) = x2 + 5


Answer the following:

Simplify `log_10  28/45 - log_10  35/324 + log_10  325/432 - log_10  13/15`


Answer the following:

Without using log tables, prove that `2/5 < log_10 3 < 1/2`


Answer the following:

Show that, logy x3 . logz y4 . logx z5 = 60


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`


Answer the following:

Find the range of the following function.

f(x) = `x/(9 + x^2)`


Given the function f: x → x2 – 5x + 6, evaluate f(2)


Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)


A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour


The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Length ‘x’ of
forehand (in cm)
Height 'y' 
(in inches)
35 56
45 65
50 69.5
55 74

Check if this relation is a function


The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.


If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______


Let f : R → R be defined by 

f(x) = `{(3x;    x > 2),(2x^2;    1 ≤ x ≤ 2), (4x;   x < 1):}`

Then f(-2) + f(1) + f(3) is ______ 


Find the domain of the following function.

f(x) = `x/(x^2 + 3x + 2)`


Find the range of the following functions given by `|x - 4|/(x - 4)`


Find the range of the following functions given by f(x) = `3/(2 - x^2)`


Let f(x) = `sqrt(1 + x^2)`, then ______.


The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.


The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.


The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×