Advertisements
Advertisements
प्रश्न
If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).
Advertisements
उत्तर
\[ = f \left( \left( 3 - x^3 \right)^\frac{1}{3} \right)\]
\[ = \left[ 3 - \left( \left( 3 - x^3 \right)^\frac{1}{3} \right)^3 \right]^\frac{1}{3} \]
\[ = \left[ 3 - \left( 3 - x^3 \right) \right]^\frac{1}{3} \]
\[ = \left( x^3 \right)^\frac{1}{3} \]
\[ = x\]
APPEARS IN
संबंधित प्रश्न
Check the injectivity and surjectivity of the following function:
f : Z → Z given by f(x) = x3
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
Find the number of all onto functions from the set {1, 2, 3, ..., n} to itself.
Prove that the function f : N → N, defined by f(x) = x2 + x + 1, is one-one but not onto
Classify the following function as injection, surjection or bijection :
f : Z → Z, defined by f(x) = x2 + x
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = x3 + 1
Classify the following function as injection, surjection or bijection :
f : Q − {3} → Q, defined by `f (x) = (2x +3)/(x-3)`
Find fog (2) and gof (1) when : f : R → R ; f(x) = x2 + 8 and g : R → R; g(x) = 3x3 + 1.
Find fog and gof if : f (x) = |x|, g (x) = sin x .
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 A = {1, 2, 3, 4}; B = {3, 5, 7, 9}; C = {7, 23, 47, 79} and f : A → B, g : B → C be defined as f(x) = 2x + 1 and g(x) = x2 − 2. Express (gof)−1 and f−1 og−1 as the sets of ordered pairs and verify that (gof)−1 = f−1 og−1.
A function f : R → R is defined as f(x) = x3 + 4. Is it a bijection or not? In case it is a bijection, find f−1 (3).
Let A = {x &epsis; R | −1 ≤ x ≤ 1} and let f : A → A, g : A → A be two functions defined by f(x) = x2 and g(x) = sin (π x/2). Show that g−1 exists but f−1 does not exist. Also, find g−1.
If f : R → R, g : R → are given by f(x) = (x + 1)2 and g(x) = x2 + 1, then write the value of fog (−3).
Let f : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]
Let f : R → R be defined as `f (x) = (2x - 3)/4.` write fo f-1 (1) .
Write the domain of the real function
`f (x) = sqrt([x] - x) .`
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 A = {a, b, c, d} and f : A → A be given by f = {( a,b ),( b , d ),( c , a ) , ( d , c )} write `f^-1`. [NCERT EXEMPLAR]
\[f : A \to \text{B given by } 3^{ f\left( x \right)} + 2^{- x} = 4\] is a bijection, then
The range of the function
\[f\left( x \right) =^{7 - x} P_{x - 3}\]
Which of the following functions form Z to itself are bijections?
Let
\[f : R \to R\] be a function defined by
Let
\[A = \left\{ x \in R : x \geq 1 \right\}\] The inverse of the function,
\[f : A \to A\] given by
\[f\left( x \right) = 2^{x \left( x - 1 \right)} , is\]
If the function
\[f : R \to R\] be such that
\[f\left( x \right) = x - \left[ x \right]\] where [x] denotes the greatest integer less than or equal to x, then \[f^{- 1} \left( x \right)\]
The distinct linear functions that map [−1, 1] onto [0, 2] are
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 D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D
Let C be the set of complex numbers. Prove that the mapping f: C → R given by f(z) = |z|, ∀ z ∈ C, is neither one-one nor onto.
Let A = R – {3}, B = R – {1}. Let f: A → B be defined by f(x) = `(x - 2)/(x - 3)` ∀ x ∈ A . Then show that f is bijective.
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 f : R → R be defind by f(x) = `1/"x" AA "x" in "R".` Then f is ____________.
Let g(x) = x2 – 4x – 5, then ____________.
Let f : R `->` R be a function defined by f(x) = x3 + 4, then f is ______.
If `f : R -> R^+ U {0}` be defined by `f(x) = x^2, x ∈ R`. The mapping is
Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R then 'f' is
Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if "n is even"):}` Is the function injective? Justify your answer.
The domain of the function `cos^-1((2sin^-1(1/(4x^2-1)))/π)` is ______.
The given function f : R → R is not ‘onto’ function. Give reason.
