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} = 0
Advertisements
उत्तर
{x} = 0
∴ x is an integer
∴ The solution set is Z.
APPEARS IN
संबंधित प्रश्न
If f(x) = 2x2 + 3, g(x) = 5x − 2, then find g ° f
Verify that f and g are inverse functions of each other, where f(x) = `(x - 7)/4`, g(x) = 4x + 7
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = 9x3 + 8
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(3)
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) = 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"(1/4)`
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.
2{x} = x + [x]
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 f ° g and g ° f : f(x) = x2 + 5, g(x) = x – 8
Answer the following:
Find f ° g and g ° f: f(x) = 3x – 2, g(x) = x2
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
|x2 − 9| + |x2 − 4| = 5
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:
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(x) if g(x) = x2 + x – 2 and (g ° f) (x) = 4x2 – 10x + 4
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)`
For f(x) = [x] , where [x] is the greatest integer function, which of the following is true, for every x ∈ R.
`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 ______
Inverse of the function y = 5 – 10x is ______.
Let f(x) = 1 + x, g(x) = x2 + x + 1, then (f + g) (x) at x = 0 is ______.
Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.
