Advertisements
Advertisements
प्रश्न
Answer the following:
Find (f ° f) (x) if f(x) = `x/sqrt(1 + x^2)`
Advertisements
उत्तर
f(x) = `x/sqrt(1 + x^2)`
∴ (f ° f) (x) = f[f(x)]
= `"f"[x/sqrt(1 + x^2)]`
= `((x/sqrt(1 + x^2)))/(sqrt(1 + (x/sqrt(1 + x^2))^2`
= `((x/sqrt(1 + x^2)))/(sqrt(1 + x^2/(1 + x^2))`
= `((x/sqrt(1 + x^2)))/(sqrt((1 + x^2 + x^2)/(1 + x^2)`
= `x/sqrt(1 + 2x^2)`
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 f ° 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) = 5x2
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = 9x3 + 8
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(2)
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(2π), where π = 3.14
If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1.2)
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.
|x| ≤ 3
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} = 0.5
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 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:
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 the domain of the following function.
f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = ex, g(x) = log x
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 ______
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) =bx - 7 and f(-1) = 4, then b = ______.
If f(x) =x4, g(x) = 6x – 2, then g[f(x)] = ______.
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 ______.
The value of `int_-1^3 (|x - 2| + [x]) dx` is equal to ______.
(where [.] denotes greatest integer function)
