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 signum function f : R → R, given by
`f(x) = {(1", if" x > 0), (0", if" x = 0), (-1", if" x < 0):}`
is neither one-one nor onto.
Show that the function f : R → {x ∈ R : –1 < x < 1} defined by f(x) = `x/(1 + |x|)`, x ∈ R is one-one and onto function.
Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x2
Classify the following function as injection, surjection or bijection :
f : Z → Z, defined by f(x) = x − 5
If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.
Let A = [-1, 1]. Then, discuss whether the following functions from A to itself is one-one, onto or bijective : h(x) = x2
Let R+ be the set of all non-negative real numbers. If f : R+ → R+ and g : R+ → R+ are defined as `f(x)=x^2` and `g(x)=+sqrtx` , find fog and gof. Are they equal functions ?
Find fog and gof if : f(x) = c, c ∈ R, g(x) = sin `x^2`
If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?
if `f (x) = sqrt(1-x)` and g(x) = `log_e` x are two real functions, then describe functions fog and gof.
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 f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.
Which one of the following graphs represents a function?
Let f be an invertible real function. Write ( f-1 of ) (1) + ( f-1 of ) (2) +..... +( f-1 of ) (100 )
What is the range of the function
`f (x) = ([x - 1])/(x -1) ?`
If f(x) = 4 −( x - 7)3 then write f-1 (x).
The function f : R → R defined by
`f (x) = 2^x + 2^(|x|)` is
A function f from the set of natural numbers to integers defined by
`{([n-1]/2," when n is odd" is ),(-n/2,when n is even ) :}`
The function f : [-1/2, 1/2, 1/2] → [-π /2,π/2], defined by f (x) = `sin^-1` (3x - `4x^3`), is
Let
\[f : R \to R\] be a function defined by
\[f : R \to R\] is defined by
\[f\left( x \right) = \frac{e^{x^2} - e^{- x^2}}{e^{x^2 + e^{- x^2}}} is\]
Which of the following functions from
\[A = \left\{ x \in R : - 1 \leq x \leq 1 \right\}\]
\[f : Z \to Z\] be given by
` f (x) = {(x/2, ", if x is even" ) ,(0 , ", if x is odd "):}`
Then, f is
Let
\[A = \left\{ x \in R : x \leq 1 \right\} and f : A \to A\] be defined as
\[f\left( x \right) = x \left( 2 - x \right)\] Then,
\[f^{- 1} \left( x \right)\] 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 \[f^{- 1} \left( x \right)\]
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
Let A = ℝ − {3}, B = ℝ − {1}. Let f : A → B be defined by \[f\left( x \right) = \frac{x - 2}{x - 3}, \forall x \in A\] Show that f is bijective. Also, find
(i) x, if f−1(x) = 4
(ii) f−1(7)
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.
Using the definition, prove that the function f: A→ B is invertible if and only if f is both one-one and onto
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:
A function f: x → y is/are called onto (or surjective) if x under f.
'If 'f' is a linear function satisfying f[x + f(x)] = x + f(x), then f(5) can be equal to:
Let f: R→R be defined as f(x) = 2x – 1 and g: R – {1}→R be defined as g(x) = `(x - 1/2)/(x - 1)`. Then the composition function f (g(x)) is ______.
Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is ______.
Write the domain and range (principle value branch) of the following functions:
f(x) = tan–1 x.
Which one of the following graphs is a function of x?
 |
 |
| Graph A | Graph B |
For \(f(x)=x^2+x\), if \(y=1\), which two domain elements have the same image?
If every seat in a classroom is occupied by one student, the situation resembles:
Which condition represents a one-one (injective) function?
