मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct answer from given alternatives The domain of 1[x]-x where [x] is greatest integer function is - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct answer from given alternatives

The domain of `1/([x] - x)` where [x] is greatest integer function is

पर्याय

  • R

  • Z

  • R − Z

  • Q - {o}

MCQ

उत्तर

R − Z

Explanation;

f(x) = `1/([x]-x)=1/(-{x})`

For f to be defined, {x} ≠ 0

∴ x cannot be an integer.

∴ Domain = R – Z

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Functions - Miscellaneous Exercise 6.1 [पृष्ठ १३०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 6 Functions
Miscellaneous Exercise 6.1 | Q I. (9) | पृष्ठ १३०

संबंधित प्रश्‍न

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

  1. {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
  2. {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
  3. {(1, 3), (1, 5), (2, 5)}

\[f\left( x \right) = \begin{cases}3x - 2, & x < 0; \\ 1, & x = 0; \\ 4x + 1, & x > 0 .\end{cases}\]

find: f(1), f(−1), f(0) and f(2).

 

 


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

(b) {x : f(x) = −2}


fgh are three function defined from R to R as follow:

(iii) h(x) = x2 + 1

Find the range of function.


If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.

 

 


Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function: 

(viii) \[\frac{5}{8}\]

 

Let f and g be two real functions given by

f = {(0, 1), (2, 0), (3, −4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}

Find the domain of fg.


Which one of the following is not a function?


The range of  \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is 

 


If f(x) = `{(x^2 + 3","  x ≤ 2),(5x + 7","  x > 2):},` then find f(3)


If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x


Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 1), (2, 1), (3, 1), (4, 1)}


Check if the relation given by the equation represents y as function of x:

x + y2 = 9


Check if the relation given by the equation represents y as function of x:

x2 − y = 25


If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b


Find the domain and range of the follwoing function.

h(x) = `sqrt(x + 5)/(5 + x)`


lf f(x) = 3(4x+1), find f(– 3)


Express the following exponential equation in logarithmic form

54° = 1


Express the following logarithmic equation in exponential form

ln e = 1


Write the following expression as a single logarithm.

`1/3 log (x - 1) + 1/2 log (x)`


Prove that logbm a = `1/"m" log_"b""a"`


If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b


Solve for x.

log2 x + log4 x + log16 x = `21/4`


Select the correct answer from given alternatives

If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to


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:

Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0


Answer the following:

Find (f ° g) (x) and (g ° f) (x)

f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`


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

Find a and b


A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)


Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______ 


Domain of function f(x) = cos–1 6x is ______.


Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.


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


The domain of the function f(x) = `sin^-1((|x| + 5)/(x^2 + 1))` is (–∞, –a] ≈ [a, ∞). Then a is equal to ______.


If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×