Advertisements
Advertisements
प्रश्न
The range of the function
\[f\left( x \right) =^{7 - x} P_{x - 3}\]
पर्याय
{1, 2, 3, 4, 5}
{1, 2, 3, 4, 5, 6}
{1, 2, 3, 4}
{1, 2, 3}
उत्तर
We know that
\[7 - x > 0; x - 3 \geq 0 \text{ and }7 - x \geq x - 3\]
\[ \Rightarrow x < 7; x \geq 3 \text{ and }2x \leq 10\]
\[ \Rightarrow x < 7; x \geq 3 \text{ and }x \leq 5\]
\[So,x = \left\{ 3, 4, 5 \right\}\]
\[\text{ Range of }f\]
\[=\left\{\ {^ \left( 7 - 3 \right)}{}{P}_\left( 3 - 3 \right) , \ {^\left( 7 - 4 \right)}{}{P}_\left( 4 - 3 \right) , {^\left( 7 - 5 \right)}{}{P} \left( {}_{5 - 3} \right) \right\}\]
\[=\left\{ 4 P_0 , 3 P_1 , 2 P_2 \right\}\]
\[=\left\{ 1, 3, 2 \right\}\]
\[=\left\{ 1, 2, 3 \right\}\]
So, the answer is (d).
APPEARS IN
संबंधित प्रश्न
Check the injectivity and surjectivity of the following function:
f: R → R given by f(x) = x2
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. Show that f is one-one.
Let f: N → N be defined by f(n) = `{((n+1)/2, ",if n is odd"),(n/2,",n is even"):}` for all n ∈ N.
State whether the function f is bijective. Justify your answer.
Show that the function f: R → R given by f(x) = x3 is injective.
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]?
Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`
If f : R → R be the function defined by f(x) = 4x3 + 7, show that f is a bijection.
If f(x) = |x|, prove that fof = f.
If f(x) = 2x + 5 and g(x) = x2 + 1 be two real functions, then describe each of the following functions:
(1) fog
(2) gof
(3) fof
(4) f2
Also, show that fof ≠ f2
Let f, g, h be real functions given by f(x) = sin x, g (x) = 2x and h (x) = cos x. Prove that fog = go (fh).
State with reason whether the following functions have inverse :
g : {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}
Let f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.
If f : R → R is defined by f(x) = x2, write f−1 (25)
If f : C → C is defined by f(x) = (x − 2)3, write f−1 (−1).
Which one the following relations on A = {1, 2, 3} is a function?
f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)} [NCERT EXEMPLAR]
Let f, g : R → R be defined by f(x) = 2x + l and g(x) = x2−2 for all x
∈ R, respectively. Then, find gof. [NCERT EXEMPLAR]
Let
\[A = \left\{ x : - 1 \leq x \leq 1 \right\} \text{and} f : A \to \text{A such that f}\left( x \right) = x|x|\]
If a function\[f : [2, \infty )\text{ to B defined by f}\left( x \right) = x^2 - 4x + 5\] is a bijection, then B =
The inverse of the function
\[f : R \to \left\{ x \in R : x < 1 \right\}\] given by
\[f\left( x \right) = \frac{e^x - e^{- x}}{e^x + e^{- x}}\] is
The distinct linear functions that map [−1, 1] onto [0, 2] are
Mark the correct alternative in the following question:
Let f : R→ R be defined as, f(x) = \[\begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\]
Then, find f( \[-\]1) + f(2) + f(4)
Which function is used to check whether a character is alphanumeric or not?
Write about strcmp() function.
Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is ______.
Let f: R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and – 3, respectively, are ______.
The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______
If f: R → R is defined by f(x) = x2 – 3x + 2, write f(f (x))
Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
{(x, y): x is a person, y is the mother of x}
Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:
k(x) = x2
Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.
Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x4, is ____________.
The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.
Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.
A = {S, D}, B = {1,2,3,4,5,6}
- Raji wants to know the number of functions from A to B. How many number of functions are possible?
If `f : R -> R^+ U {0}` be defined by `f(x) = x^2, x ∈ R`. The mapping is
Function f: R → R, defined by f(x) = `x/(x^2 + 1)` ∀ x ∈ R is not
The solution set of the inequation log1/3(x2 + x + 1) + 1 > 0 is ______.
Let f(x) be a polynomial function of degree 6 such that `d/dx (f(x))` = (x – 1)3 (x – 3)2, then
Assertion (A): f(x) has a minimum at x = 1.
Reason (R): When `d/dx (f(x)) < 0, ∀ x ∈ (a - h, a)` and `d/dx (f(x)) > 0, ∀ x ∈ (a, a + h)`; where 'h' is an infinitesimally small positive quantity, then f(x) has a minimum at x = a, provided f(x) is continuous at x = a.
