हिंदी

If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(-52) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

f(x) = 4[x] − 3

`"f"(- 5/2)`

= `4[− 5/2] − 3`

= 4(− 3) − 3    

= − 15

shaalaa.com
Algebra of Functions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Exercise 6.2 [पृष्ठ १२८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Exercise 6.2 | Q 9. (c) | पृष्ठ १२८

संबंधित प्रश्न

Verify that f and g are inverse functions of each other, where f(x) = x3 + 4, g(x) = `root(3)(x - 4)`


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(2)


If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(0)


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(5)


If f(x) = 2|x| + 3x, then find f(2)


If f(x) = 2|x| + 3x, then find f(– 5)


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.

|x − 4| + |x − 2| = 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 + [x + [x]]] = 9


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 composite of f and g:
f = {(1, 1), (2, 4), (3, 4), (4, 3)}
g = {(1, 1), (3, 27), (4, 64)}


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

−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/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 ° f) (x) if f(x) = `x/sqrt(1 + x^2)`


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 ______.


If f(x) = `sin^2x + sin^2(x + pi/3) + cosx cos(x + pi/3) and g(5/4) = 1`, then (gof)(x) is equal to: ______ 


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 value of `int_-1^3 (|x - 2| + [x])  dx` is equal to ______.

(where [.] denotes greatest integer function)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×