हिंदी

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 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

−2 < [x] ≤ 7

∴ −1 ≤ x < 8

Solution set = [–1, 8)

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Miscellaneous Exercise 6.2 [पृष्ठ १३१]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 6 Functions
Miscellaneous Exercise 6.2 | Q II. (39) (d) | पृष्ठ १३१

संबंधित प्रश्न

If f(x) = 2x2 + 3, g(x) = 5x − 2, then find g ° f


If f(x) = 2x2 + 3, g (x) = 5x − 2, then find g ° g


Verify that f and g are inverse functions of each other, where f(x) = `(x + 3)/(x - 2)`, g(x) = `(2x + 3)/(x - 1)`


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

f(x) = 8


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

f(x) = 9x3 + 8


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


If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(1)


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


If f(x) = 2|x| + 3x, then find f(2)


If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(7.2)


If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find `"f"(- 5/2)`


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| ≥ 5


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| ≤ 3


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.

{x} = 0


Answer the following:

Find whether the following function is onto or not.

f : R → R defined by f(x) = x2 + 3 for all x ∈ R


Answer the following:

Find composite of f and g:
f = {(1, 1), (2, 4), (3, 4), (4, 3)}
g = {(1, 1), (3, 27), (4, 64)}


Answer the following:

Find f ° g and g ° f : f(x) = x2 + 5, g(x) = x – 8


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[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

[x − 2] + [x + 2] + {x} = 0


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`


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) = `x/sqrt(1 + x^2)`


For f(x) = [x] , where [x] is the greatest integer function, which of the following is true, for every x ∈ R.


If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof is ______ 


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


Inverse of the function y = 5 – 10x is ______.


`int_0^3 [x]dx` = ______, where [x] is 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×