Advertisements
Advertisements
प्रश्न
If f : R `rightarrow` R is defined by `f(x) = (2x - 7)/4`, show that f(x) is one-one and onto.
Advertisements
उत्तर
Given, `f(x) = (2x - 7)/4`
For one-one
Let x, x2 ∈ R
f(x1) = f(x2)
`(2x_1 - 7)/4 = (2x_2 - 7)/4`
`\implies` 2x1 – 7 = 2x2 – 7
`\implies` 2x1 = 2x2
`\implies` x1 = x2
So, f(x) is a one-to-one function.
For onto
Put `y = (2x - 7)/4`
`\implies` 4y = 2x – 7
`\implies` 4y + 7 = 2x
`\implies` `x = (4y + 7)/2` ∀ y ∈ R ∃ a unique x ∈ R
Therefore, f(x) is onto.
APPEARS IN
संबंधित प्रश्न
Show that the function f : R → R given by f(x) = x3 is injective.
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, 2), (b, 1), (c, 1)}
Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : g(x) = |x|
If f : R → R be defined by f(x) = x3 −3, then prove that f−1 exists and find a formula for f−1. Hence, find f−1(24) and f−1 (5).
Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {a, b, c}.
If f : R → R is defined by f(x) = x2, find f−1 (−25).
If f : R → R is defined by f(x) = 10 x − 7, then write f−1 (x).
Write the domain of the real function
`f (x) = 1/(sqrt([x] - x)`.
The function
f : A → B defined by
f (x) = - x2 + 6x - 8 is a bijection if
Let f be an injective map with domain {x, y, z} and range {1, 2, 3}, such that exactly one of the following statements is correct and the remaining are false.
\[f\left( x \right) = 1, f\left( y \right) \neq 1, f\left( z \right) \neq 2 .\]
The value of
\[f^{- 1} \left( 1 \right)\] 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,
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)
Write about strlen() function.
The smallest integer function f(x) = [x] is ____________.
Consider a set containing function A= {cos–1cosx, sin(sin–1x), sinx((sinx)2 – 1), etan{x}, `e^(|cosx| + |sinx|)`, sin(tan(cosx)), sin(tanx)}. B, C, D, are subsets of A, such that B contains periodic functions, C contains even functions, D contains odd functions then the value of n(B ∩ C) + n(B ∩ D) is ______ where {.} denotes the fractional part of functions)
Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.
The graph of the function y = f(x) is symmetrical about the line x = 2, then ______.
Which one of the following graphs is a function of x?
 |
 |
| Graph A | Graph B |
In the function from \(X\) to \(Y\), if \(6\in Y\) is not the image of any element of \(X\), the function is:
