Advertisements
Advertisements
Question
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`
Advertisements
Solution
`[x/2] + [x/3] = (5x)/6`
L.H.S. = an integer
∴ R.H.S. = an integer
∴ x = 6k, where k is an integer
APPEARS IN
RELATED QUESTIONS
If f(x) = 2x2 + 3, g (x) = 5x − 2, then find f ° g
If f(x) = 2x2 + 3, g(x) = 5x − 2, then find f ° 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 - 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) = 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) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
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) = 2|x| + 3x, then find f(– 5)
If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1)
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.
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 + [x + [x]]] = 9
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 : R → R defined by f(x) = x2 + 3 for all x ∈ R
Answer the following:
Find composite of f and g:
f = {(1, 3), (2, 4), (3, 5), (4, 6)}
g = {(3, 6), (4, 8), (5, 10), (6, 12)}
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) = 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] − 5[x] + 6 = 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`
The inverse of the function y = `(16^x - 16^-x)/(16^x + 16^-x)` is
`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 ______
Let F(x) = ex, G(x) = e-x and H(x) = G[F(x)], where x is a real variable. Then `"dH"/"dx"`at x = 0 is ______.
Let f(x) = 1 + x, g(x) = x2 + x + 1, then (f + g) (x) at x = 0 is ______.
The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` is ______.
Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.
