हिंदी

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(14) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find `"f"(1/4)`

योग

उत्तर

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

`{1/4} = 1/4 - [1/4]`

= `1/4 - 0`

= `1/4`

`"f"(1/4) = 2{1/4} + 5(1/4)`

= `2(1/4) + 5/4`

= `7/4`

= 1.75

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 10. (b) | पृष्ठ १२८

संबंधित प्रश्न

Let f : {2, 4, 5} → {2, 3, 6} and g : {2, 3, 6} → {2, 4} be given by f = {(2, 3), (4, 6), (5, 2)} and g = {(2, 4), (3, 4), (6, 2)}. Write down g ° 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) = 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) = 8


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(– 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) = 2|x| + 3x, then find f(– 5)


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"(- 5/2)`


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 + [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) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (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

[x2] − 5[x] + 6 = 0


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


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 ______.


lf f : [1, ∞) `rightarrow` [2, ∞) is given by f(x) = `x + 1/x`, then f–1(x) is equal to ______.


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×