Advertisements
Advertisements
प्रश्न
Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then ______.
विकल्प
f–1(x) = f(x)
f–1(x) = – f(x)
(f o f)x = – x
f–1(x) = `1/19` f(x)
Advertisements
उत्तर
Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then f–1(x) = f(x).
Explanation:
We have f(x) = `(3x + 2)/(5x - 3)` = y ......(Let)
⇒ 3x + 2 = 5xy – 3y
⇒ x(3 – 5y) = –3y – 2
⇒ x = `(3y + 2)/(5y - 3)`
⇒ f–1(x) = `(3x + 2)/(5x - 3)`
∴ f–1(x) = f(x)
APPEARS IN
संबंधित प्रश्न
Show that the function f : R* → R* defined by f(x) = `1/x` is one-one and onto, where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R?
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by f(x) = `((x - 2)/(x - 3))`. Is f one-one and onto? Justify your answer.
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = x3 − x
Classify the following function as injection, surjection or bijection :
f : Q − {3} → Q, defined by `f (x) = (2x +3)/(x-3)`
Set of ordered pair of a function ? If so, examine whether the mapping is injective or surjective :{(a, b) : a is a person, b is an ancestor of a}
If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.
If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.
If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.
Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1
Let f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.
If A = {1, 2, 3, 4} and B = {a, b, c, d}, define any four bijections from A to B. Also give their inverse functions.
Let A and B be two sets, each with a finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.
If f : A → A, g : A → A are two bijections, then prove that fog is an injection ?
If f : A → A, g : A → A are two bijections, then prove that fog is a surjection ?
Let A = {x ∈ R : −4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\]Write the range of f.
Let f : R → R be defined as `f (x) = (2x - 3)/4.` write fo f-1 (1) .
The function
f : A → B defined by
f (x) = - x2 + 6x - 8 is a bijection if
Let M be the set of all 2 × 2 matrices with entries from the set R of real numbers. Then, the function f : M→ R defined by f(A) = |A| for every A ∈ M, is
Which of the following functions from
to itself are bijections?
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 function f : [-1/2, 1/2, 1/2] → [-π /2,π/2], defined by f (x) = `sin^-1` (3x - `4x^3`), is
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
If \[F : [1, \infty ) \to [2, \infty )\] is given by
\[f\left( x \right) = x + \frac{1}{x}, then f^{- 1} \left( x \right)\]
Let [x] denote the greatest integer less than or equal to x. If \[f\left( x \right) = \sin^{- 1} x, g\left( x \right) = \left[ x^2 \right]\text{ and } h\left( x \right) = 2x, \frac{1}{2} \leq x \leq \frac{1}{\sqrt{2}}\]
Let R be the set of real numbers and f: R → R be the function defined by f(x) = 4x + 5. Show that f is invertible and find f–1.
Which of the following functions from Z into Z are bijections?
The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.
The smallest integer function f(x) = [x] is ____________.
Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) is
Let g(x) = x2 – 4x – 5, then ____________.
Range of `"f"("x") = sqrt((1 - "cos x") sqrt ((1 - "cos x")sqrt ((1 - "cos x")....infty))`
Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is ____________.
A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever
Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}
- Mr. ’X’ and his wife ‘W’ both exercised their voting right in the general election-2019, Which of the following is true?
Let f: R → R defined by f(x) = x4. Choose the correct answer
Let n(A) = 4 and n(B) = 6, Then the number of one – one functions from 'A' to 'B' is:
Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R then 'f' is
The solution set of the inequation log1/3(x2 + x + 1) + 1 > 0 is ______.
If A = {x ∈ R: |x – 2| > 1}, B = `{x ∈ R : sqrt(x^2 - 3) > 1}`, C = {x ∈ R : |x – 4| ≥ 2} and Z is the set of all integers, then the number of subsets of the set (A ∩ B ∩ C) C ∩ Z is ______.
