Advertisements
Advertisements
Question
Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D
Advertisements
Solution
Given real valued function f(x), such that f(x) = `sqrt(25 - x^2)`
Since f(x) is reaal valued
We must have
25 – x2 ≥ 0
⇒ x2 ≤ 25
⇒ – 5 ≤ x ≤ 5
⇒ The Domain D = [–5, 5]
APPEARS IN
RELATED QUESTIONS
Show that the function f in `A=R-{2/3} ` defined as `f(x)=(4x+3)/(6x-4)` is one-one and onto hence find f-1
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?
Check the injectivity and surjectivity of the following function:
f : N → N given by f(x) = x3
Let S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.
F = {(a, 3), (b, 2), (c, 1)}
If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`
Give an example of a function which is not one-one but onto ?
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) = x − 5
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = sin2x + cos2x
If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.
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}
Show that the exponential function f : R → R, given by f(x) = ex, is one-one but not onto. What happens if the co-domain is replaced by`R0^+` (set of all positive real numbers)?
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 onto functions, show that gof is a onto function.
Find fog and gof if : f (x) = x2 g(x) = cos x .
Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.
Consider the function f : R+ → [-9 , ∞ ]given by f(x) = 5x2 + 6x - 9. Prove that f is invertible with f -1 (y) = `(sqrt(54 + 5y) -3)/5` [CBSE 2015]
If f : R → (0, 2) defined by `f (x) =(e^x - e^(x))/(e^x +e^(-x))+1`is invertible , find f-1.
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 : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).
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) .`
Write the domain of the real function
`f (x) = 1/(sqrt([x] - x)`.
If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then find fog. [NCERT EXEMPLAR]
\[f : A \to \text{B given by } 3^{ f\left( x \right)} + 2^{- x} = 4\] is a bijection, then
Let
\[f : [2, \infty ) \to X\] be defined by
\[f\left( x \right) = 4x - x^2\] Then, f is invertible if X =
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
Mark the correct alternative in the following question:
Let A = {1, 2, ... , n} and B = {a, b}. Then the number of subjections from A into B is
Mark the correct alternative in the following question:
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is
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,
Write about strlen() function.
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.
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 X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not
h = {(1,4), (2, 5), (3, 5)}
If N be the set of all-natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is ____________.
The function f: R → R defined as f(x) = x3 is:
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. Based on the given information, f is best defined as:
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 ______.
If every seat in a classroom is occupied by one student, the situation resembles:
