हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग

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
Algebra of Functions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Exercise 6.2 [पृष्ठ १२७]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Exercise 6.2 | Q 3. (d) | पृष्ठ १२७

संबंधित प्रश्न

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


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


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


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(– 4)


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


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)


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(2π), where π = 3.14


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"(1/4)`


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.

2{x} = x + [x]


Answer the following:

Find whether the following function is onto or not.

f : R → R defined by f(x) = x2 + 3 for all x ∈ R


Answer the following:

Find composite of f and g:
f = {(1, 3), (2, 4), (3, 5), (4, 6)}
g = {(3, 6), (4, 8), (5, 10), (6, 12)}


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:

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

|x2 − x − 6| = x + 2


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[2x − 5] − 1 = 7


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`


Answer the following:

Find f(x) if g(x) = `1 + sqrt(x)` and f[g(x)] = `3 + 2sqrt(x) + x`


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


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 = ______.


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 ______.


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)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×