Advertisements
Advertisements
प्रश्न
The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x; is continuous at ______.
पर्याय
x = 1
x = 1.5
x = – 2
x = 1
Advertisements
उत्तर
The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x; is continuous at x = 1.5.
Explanation:
We know that the biggest integer function is continuous only on non-integral points, not on integers.
APPEARS IN
संबंधित प्रश्न
Let f : N → N be defined by f(n) = `{((n+1)/2", if n is odd"),(n/2", if n is even"):}` for all n ∈ N.
State whether the function f is bijective. Justify your answer.
Let f: R → R be the Signum Function defined as
f(x) = `{(1,x>0), (0, x =0),(-1, x< 0):}`
and g: R → R be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0, 1]?
If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.
Show that f : R→ R, given by f(x) = x — [x], is neither one-one nor onto.
Let
f (x) =`{ (1 + x, 0≤ x ≤ 2) , (3 -x , 2 < x ≤ 3):}`
Find fof.
Consider f : R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^-1 (x) = (sqrt (x +6)-1)/3 .`
If A = {1, 2, 3} and B = {a, b}, write the total number of functions from A to B.
Let `f : R - {- 3/5}` → R be a function defined as `f (x) = (2x)/(5x +3).`
f-1 : Range of f → `R -{-3/5}`.
Write the domain of the real function
`f (x) = sqrt([x] - x) .`
If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).
Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not.
The function
f : A → B defined by
f (x) = - x2 + 6x - 8 is a bijection if
Let
f : R → R be given by
\[f\left( x \right) = \left[ x^2 \right] + \left[ x + 1 \right] - 3\]
where [x] denotes the greatest integer less than or equal to x. Then, f(x) is
(d) one-one and onto
Let f be an injective map with domain {x, y, z} and range {1, 2, 3}, such that exactly one of the following statements is correct and the remaining are false.
\[f\left( x \right) = 1, f\left( y \right) \neq 1, f\left( z \right) \neq 2 .\]
The value of
\[f^{- 1} \left( 1 \right)\] is
If \[F : [1, \infty ) \to [2, \infty )\] is given by
\[f\left( x \right) = x + \frac{1}{x}, then f^{- 1} \left( x \right)\]
If \[f : R \to \left( - 1, 1 \right)\] is defined by
\[f\left( x \right) = \frac{- x|x|}{1 + x^2}, \text{ then } f^{- 1} \left( x \right)\] equals
Let
\[f : R \to R\] be given by \[f\left( x \right) = x^2 - 3\] Then, \[f^{- 1}\] is given by
Which function is used to check whether a character is alphanumeric or not?
Write about strlen() function.
Write about strcmp() function.
For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is surjective. Then g is surjective.
Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D
Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1
The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.
Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.
Answer the following questions using the above information.
- Let f: R → R be defined by f(x) = x2 is:
A function f: x → y is said to be one – one (or injective) if:
A function f: x → y is/are called onto (or surjective) if x under f.
Let f: R→R be a continuous function such that f(x) + f(x + 1) = 2, for all x ∈ R. If I1 = `int_0^8f(x)dx` and I2 = `int_(-1)^3f(x)dx`, then the value of I1 + 2I2 is equal to ______.
For x ∈ R, x ≠ 0, let f0(x) = `1/(1 - x)` and fn+1 (x) = f0(fn(x)), n = 0, 1, 2, .... Then the value of `f_100(3) + f_1(2/3) + f_2(3/2)` is equal to ______.
Let A = R – {2} and B = R – {1}. If f: A `→` B is a function defined by f(x) = `(x - 1)/(x - 2)` then show that f is a one-one and an onto function.
