मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

If f(x) = 2x2 + 3, g(x) = 5x − 2, then find f ° f - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If f(x) = 2x2 + 3, g(x) = 5x − 2, then find f ° f

बेरीज
Advertisements

उत्तर

f(x) = 2x2 + 3, g(x) = 5x − 2

(f ° f) (x) = f[f(x)]

= f(2x2 + 3)

= 2(2x2 + 3)2 + 3

= 2(4x4 + 12x2 + 9) + 3

= 8x4 + 24x2 + 21

shaalaa.com
Algebra of Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Functions - Exercise 6.2 [पृष्ठ १२७]

APPEARS IN

संबंधित प्रश्‍न

If f(x) = 2x2 + 3, g(x) = 5x − 2, then find 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) = `(6x - 7)/3`


Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = `sqrt(4x + 5)`


Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`


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(– 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(– 1.2)


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| + |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


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


Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

2{x} = x + [x]


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) = 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:

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:

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


For f(x) = [x] , where [x] is the greatest integer function, which of the following is true, for every x ∈ R.


`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 ______ 


If z ≠ 0, then `int_(x = 0)^100` [arg | z |] dx is ______.

(where [.] denotes the greatest integer function)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×