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
|x2 − x − 6| = x + 2
Advertisements
Solution
|x2 − x − 6| = x + 2 ...(i)
R.H.S. must be non-negative
∴ x ≥ − 2 ...(ii)
|(x – 3) (x + 2)| = x + 2
∴ (x + 2) |x – 3| = x + 2 as x + 2 ≥ 0
∴ |x – 3| = 1 if x ≠ – 2
∴ x – 3 = ± 1
∴ x = 4 or 2
∴ x = – 2 also satisfies the equation
Solution set = {–2, 2, 4}
APPEARS IN
RELATED QUESTIONS
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 + 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) = 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(1)
If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(5)
If f(x) = 2|x| + 3x, then find f(2)
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"(- 5/2)`
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.
|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
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} > 4
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} = 0.5
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 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:
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 − 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
−2 < [x] ≤ 7
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:
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) = `x/sqrt(1 + x^2)`
If `a + pi/2 < 2tan^-1x + 3cot^-1x < b`, then a and b are respectively.
`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 ______
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)
Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.
