हिंदी

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function. |x| ≤ 3 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

|x| ≤ 3

योग

उत्तर

|x| ≤ 3

The solution set of |x| ≤ a is

– a ≤ x ≤ a

∴ The required solution is – 3 ≤ x ≤ 3

∴ The solution set is [– 3, 3]

shaalaa.com
Algebra of Functions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Exercise 6.2 [पृष्ठ १२८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Exercise 6.2 | Q 11. (d) | पृष्ठ १२८

संबंधित प्रश्न

Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = 5x2


Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = `(6x - 7)/3`


Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = `sqrt(4x + 5)`


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


If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(– 4)


If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(– 3)


If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(5)


If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(0.5)


If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1.2)


If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 6)


Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

|x − 4| + |x − 2| = 3


Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

x2 + 7 |x| + 12 = 0


Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

{x} > 4


Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

2{x} = x + [x]


Answer the following:

Find f ° g and g ° f: f(x) = 256x4, g(x) = `sqrt(x)`


Answer the following:

If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (x) = x


Answer the following:

If f(x) = `(x + 3)/(4x - 5)`, g(x) = `(3 + 5x)/(4x - 1)` then show that (f ° g) (x) = x


Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

1 < |x − 1| < 4


Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

|x2 − x − 6| = x + 2


Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

−2 < [x] ≤ 7


Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

2[2x − 5] − 1 = 7


Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

[x2] − 5[x] + 6 = 0


Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

[x − 2] + [x + 2] + {x} = 0


Answer the following:

Find f(x) if g(x) = `1 + sqrt(x)` and f[g(x)] = `3 + 2sqrt(x) + x`


Answer the following:

Find (f ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`


The inverse of the function y = `(16^x - 16^-x)/(16^x + 16^-x)` is


If `a + pi/2 < 2tan^-1x + 3cot^-1x < b`, then a and b are respectively.


`int_0^4 x[x]  dx`, where [.] denotes the greatest integer function, equals ______


If f(x) =x4, g(x) = 6x – 2, then g[f(x)] = ______.


The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` is ______.


If g(x) is the inverse function of f(x) and f'(x) = `1/(1 + x^4)`, then g'(x) is ______.


lf f : [1, ∞) `rightarrow` [2, ∞) is given by f(x) = `x + 1/x`, then f–1(x) is equal to ______.


If z ≠ 0, then `int_(x = 0)^100` [arg | z |] dx is ______.

(where [.] denotes the greatest integer function)


The value of `int_-1^3 (|x - 2| + [x])  dx` is equal to ______.

(where [.] denotes greatest integer function)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×