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

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

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

f(x) = 2x2 + 3, g (x) = 5x − 2

(g ° g) (x) = g[g(x)]

= g(5x − 2)

= 5(5x − 2) − 2

= 25x − 12

shaalaa.com
  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 f ° g


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) = `(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) = `(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(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) = 4[x] − 3, where [x] is greatest integer function of x, then find f(7.2)


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| ≤ 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} = 0


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:

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

[x2] − 5[x] + 6 = 0


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(1 - sqrt(1 - 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.


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: ______ 


If f(x) =bx - 7 and f(-1) = 4, then b = ______.


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 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×