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} > 4
Advertisements
उत्तर
{x} > 4
∵ 0 ≤ {x} < 1
∴ {x} > 4 has no solution
∴ solution set is { }
APPEARS IN
संबंधित प्रश्न
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) = `(6x - 7)/3`
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = `sqrt(4x + 5)`
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) = 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(– 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.
2|x| = 5
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 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:
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
[x2] − 5[x] + 6 = 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 ° 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(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)`
If f(x) =x4, g(x) = 6x – 2, then g[f(x)] = ______.
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 ______.
The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` 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.
Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.
