English

The given function f : R → R is not ‘onto’ function. Give reason.

Advertisements
Advertisements

Question


The given function f : R → R is not ‘onto’ function. Give reason.

Graph
Advertisements

Solution

Since each line in co-domain of the function parallel to x-axis, doesn’t cuts the graph of function at least one point, therefore the f(x) is not an onto function.

shaalaa.com
  Is there an error in this question or solution?
2024-2025 (March) Specimen Paper

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

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.


Let A = {−1, 0, 1} and f = {(xx2) : x ∈ A}. Show that f : A → A is neither one-one nor onto.


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.


Show that f : R→ R, given by f(x) = x — [x], is neither one-one nor onto.


If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.


Find fog and gof  if : f(x) = `x^2` + 2 , g (x) = 1 − `1/ (1-x)`.


Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {abc}.


If f : C → C is defined by f(x) = x2, write f−1 (−4). Here, C denotes the set of all complex numbers.


If f : C → C is defined by f(x) = x4, write f−1 (1).


Let f : R → Rg : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 − x2. Write fog (−2).


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 ) :}`

 

 


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

 


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.


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

f = {(1, 4), (1, 5), (2, 4), (3, 5)}


Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

f(x) = `x/2`


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 said to be one – one (or injective) if:


Consider a function f: `[0, pi/2] ->` R, given by f(x) = sinx and `g[0, pi/2] ->` R given by g(x) = cosx then f and g are


The solution set of the inequation log1/3(x2 + x + 1) + 1 > 0 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×