English

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function. {x} > 4 - Mathematics and Statistics

Advertisements
Advertisements

Question

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

{x} > 4

Sum

Solution

{x} > 4

∵ 0 ≤ {x} < 1

∴ {x} > 4 has no solution

∴ solution set is {  }

shaalaa.com
Algebra of Functions
  Is there an error in this question or solution?
Chapter 6: Functions - Exercise 6.2 [Page 128]

RELATED QUESTIONS

Let f : {2, 4, 5} → {2, 3, 6} and g : {2, 3, 6} → {2, 4} be given by f = {(2, 3), (4, 6), (5, 2)} and g = {(2, 4), (3, 4), (6, 2)}. Write down g ° f


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) = x3 + 4, g(x) = `root(3)(x - 4)`


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) = 8


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) = 9x3 + 8


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


If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(0)


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


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.

|x| ≤ 3


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

2|x| = 5


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 f ° g and g ° f: f(x) = 3x – 2, g(x) = x2


Answer the following:

Find f ° g and g ° f: f(x) = 256x4, g(x) = `sqrt(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[2x − 5] − 1 = 7


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 ° g) (x) and (g ° f) (x)

f(x) = ex, g(x) = log x


Answer the following:

Find (f ° f) (x) if f(x) = `x/sqrt(1 + x^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.


If f(x) =bx - 7 and f(-1) = 4, then b = ______.


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


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


`int_0^3 [x]dx` = ______, where [x] is greatest integer function.


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×