English

The domain of the function f: R → R defined by f(x) = x2-3x+2 is ______

Advertisements
Advertisements

Question

The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______

Fill in the Blanks
Advertisements

Solution

Here x2 – 3x + 2 ≥ 0

⇒ (x – 1)(x – 2) ≥ 0

⇒ x ≤ 1 or x ≥ 2

Hence the domain of f = `(– oo, 1] ∪ [2, oo)`

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Relations And Functions - Solved Examples [Page 10]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 1 Relations And Functions
Solved Examples | Q 26 | Page 10

RELATED QUESTIONS

Give an example of a function which is one-one but not onto ?


Classify the following function as injection, surjection or bijection :

 f : Z → Z, defined by f(x) = x − 5 


If f : R → R be the function defined by f(x) = 4x3 + 7, show that f is a bijection.


Show that if f1 and f2 are one-one maps from R to R, then the product f1 × f2 : R → R defined by (f1 × f2) (x) = f1 (x) f2 (x) need not be one - one.


Suppose f1 and f2 are non-zero one-one functions from R to R. Is `f_1 / f^2` necessarily one - one? Justify your answer. Here,`f_1/f_2 : R → R   is   given   by   (f_1/f_2) (x) = (f_1(x))/(f_2 (x))  for all  x in R .`


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x and g(x) = |x| .


Verify associativity for the following three mappings : f : N → Z0 (the set of non-zero integers), g : Z0 → Q and h : Q → R given by f(x) = 2xg(x) = 1/x and h(x) = ex.


Give examples of two functions f : N → Z and g : Z → Z, such that gof is injective but gis not injective.


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 .


 If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x|- x, ∀x∈R" .Then find fog and gof. Hence find fog(–3), fog(5) and gof (–2).


Consider the function f : R→  [-9 , ∞ ]given by f(x) = 5x2 + 6x - 9. Prove that f is invertible with -1 (y) = `(sqrt(54 + 5y) -3)/5`             [CBSE 2015]


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


Let f be an invertible real function. Write ( f-1  of ) (1) + ( f-1  of ) (2) +..... +( f-1 of ) (100 )


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]


Let fg : R → R be defined by f(x) = 2x + l and g(x) = x2−2 for all x

∈ R, respectively. Then, find gof.  [NCERT EXEMPLAR]


\[f : R \to R \text{given by} f\left( x \right) = x + \sqrt{x^2} \text{ is }\]

 

 


Let

\[f : R - \left\{ n \right\} \to R\]

\[f\left( x \right) = \frac{x - m}{x - n}, \text{where} \ m \neq n .\] Then,
 

The function \[f : R \to R\] defined by

\[f\left( x \right) = 6^x + 6^{|x|}\] is 

 


The inverse of the function

\[f : R \to \left\{ x \in R : x < 1 \right\}\] given by

\[f\left( x \right) = \frac{e^x - e^{- x}}{e^x + e^{- x}}\] is 

 


Let  \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] Then, for what value of α is \[f \left( f\left( x \right) \right) = x?\]

 


Let

\[f : [2, \infty ) \to X\] be defined by

\[f\left( x \right) = 4x - x^2\] Then, f is invertible if X =

 


If  \[f\left( x \right) = \sin^2 x\] and the composite function   \[g\left( f\left( x \right) \right) = \left| \sin x \right|\] then g(x) is equal to


A function f: R→ R defined by f(x) = `(3x) /5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f−1.


If f: R → R is defined by f(x) = x2 – 3x + 2, write f(f (x))


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

k = {(1,4), (2, 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 f: R → R be given by f(x) = tan x. Then f–1(1) is ______.


Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Raji wants to know the number of functions from A to B. How many number of functions are possible?

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.

Answer the following questions using the above information.

  • Let : N → R be defined by f(x) = x2. Range of the function among the following is ____________.

A function f: x → y is said to be one – one (or injective) if:


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 ______.


If f: [0, 1]→[0, 1] is defined by f(x) = `(x + 1)/4` and `d/(dx) underbrace(((fofof......of)(x)))_("n"  "times")""|_(x = 1/2) = 1/"m"^"n"`, m ∈ N, then the value of 'm' is ______.


Let a function `f: N rightarrow N` be defined by

f(n) = `{:[(2n",", n = 2","  4","  6","  8","......),(n - 1",", n = 3","  7","  11","  15","......),((n + 1)/2",", n = 1","  5","  9","  13","......):}`

then f is ______.


Which one of the following graphs is a function of x?

Graph A Graph B

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×