Advertisements
Advertisements
प्रश्न
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]
Advertisements
उत्तर
We have ,
A = {a, b, c, d} and f : A
→ A be given by f = {(a, b), (b, d), (c, a), (d, c)}
Since, the elements of a function when interchanged gives inverse function.
so, f -1 = {(b, a), (d, b), (a, c), (c, d)}
APPEARS IN
संबंधित प्रश्न
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.
Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.
Find gof and fog when f : R → R and g : R → R is defined by f(x) = x and g(x) = |x| .
Find fog and gof if : f (x) = x+1, g(x) = `e^x`
.
Find fog and gof if : f(x)= x + 1, g (x) = 2x + 3 .
Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.
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:
h : {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}
If f : R → (0, 2) defined by `f (x) =(e^x - e^(x))/(e^x +e^(-x))+1`is invertible , find f-1.
Let f be a function from C (set of all complex numbers) to itself given by f(x) = x3. Write f−1 (−1).
If f : R → R is defined by f(x) = x2, find f−1 (−25).
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 → R be defined as `f (x) = (2x - 3)/4.` write fo 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]
If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]
Which of the following functions form Z to itself are bijections?
If the function\[f : R \to \text{A given by} f\left( x \right) = \frac{x^2}{x^2 + 1}\] is a surjection, then A =
The function
Let \[f\left( x \right) = x^2 and g\left( x \right) = 2^x\] Then, the solution set of the equation
Let \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] Then, for what value of α is \[f \left( f\left( x \right) \right) = x?\]
If \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to
Mark the correct alternative in the following question:
Let f : R \[-\] \[\left\{ \frac{3}{5} \right\}\] \[\to\] R be defined by f(x) = \[\frac{3x + 2}{5x - 3}\] Then,
If f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)` then verify that `("fog") (x)` = x.
Which function is used to check whether a character is alphanumeric or not?
Let f: R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and – 3, respectively, are ______.
Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1
The smallest integer function f(x) = [x] is ____________.
The domain of the function `"f"("x") = 1/(sqrt ({"sin x"} + {"sin" ( pi + "x")}))` where {.} denotes fractional part, is
The function f: R → R defined as f(x) = x3 is:
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}
- Three friends F1, F2, and F3 exercised their voting right in general election-2019, then which of the following is true?
If f: R → R given by f(x) =(3 − x3)1/3, find f0f(x)
Function f: R → R, defined by f(x) = `x/(x^2 + 1)` ∀ x ∈ R is not
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 ______.
The trigonometric equation tan–1x = 3tan–1 a has solution for ______.
For \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=1+x^2\), which statement is correct?
Which condition represents a many-one function?
