English

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 6)

Advertisements
Advertisements

Question

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 6)

Sum
Advertisements

Solution

f(x) = 2{x} + 5x

{– 6} = – 6 – [– 6]

= – 6 + 6

= 0

f(– 6) = 2{– 6} + 5(– 6)

= 2(0) – 30

= – 30

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Functions - Exercise 6.2 [Page 128]

RELATED QUESTIONS

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)`


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) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(1)


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(0.5)


If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find `"f"(- 5/2)`


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)


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:

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

`[x/2] + [x/3] = (5x)/6`


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.


If `a + pi/2 < 2tan^-1x + 3cot^-1x < b`, then a and b are respectively.


If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof is ______ 


If f(x) =x4, g(x) = 6x – 2, then g[f(x)] = ______.


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 ______.


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)


Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×