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} = 0.5
Solution
{x} = 0.5
∴ x – |x| = 0.5
It is obvious that
x = m + 0.5, m ∈ Z.
APPEARS IN
RELATED QUESTIONS
If f(x) = 2x2 + 3, g(x) = 5x − 2, then find g ° f
If f(x) = 2x2 + 3, g(x) = 5x − 2, then find f ° f
Verify that f and g are inverse functions of each other, where f(x) = `(x - 7)/4`, g(x) = 4x + 7
Verify that f and g are inverse functions of each other, where f(x) = x3 + 4, g(x) = `root(3)(x - 4)`
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) = `(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) = `{(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(1)
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) = 4[x] − 3, where [x] is greatest integer function of x, then find f(2π), where π = 3.14
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| ≥ 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
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} > 4
Answer the following:
Find whether the following function is onto or not.
f : Z → Z defined by f(x) = 6x – 7 for all x ∈ Z
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:
If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (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
`[x/2] + [x/3] = (5x)/6`
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = ex, g(x) = log x
Answer the following:
Find f(x) if g(x) = x2 + x – 2 and (g ° f) (x) = 4x2 – 10x + 4
Answer the following:
Find (f ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`
`int_0^4 x[x] dx`, where [.] denotes the greatest integer function, equals ______
If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof 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.
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)
