हिंदी

Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}Determine Which of the Set Are Functions from X to Y.(C) F3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)} - Mathematics

Advertisements
Advertisements

प्रश्न

Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.

(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

 

 

उत्तर

(c) Given:
f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
f3 is not a function from X to Y because 2 ∈ X has two images, 9 and 11, in Y.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Functions - Exercise 3.1 [पृष्ठ ८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 3 Functions
Exercise 3.1 | Q 11.3 | पृष्ठ ८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Define a function as a correspondence between two sets.

 

What is the fundamental difference between a relation and a function? Is every relation a function?


Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?


If  \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.

 

 


If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.

 

 


Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function: 

(viii) \[\frac{5}{8}\]

 

If fg and h are real functions defined by 

\[f\left( x \right) = \sqrt{x + 1}, g\left( x \right) = \frac{1}{x}\] and h(x) = 2x2 − 3, find the values of (2f + g − h) (1) and (2f + g − h) (0).
 
 

Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + gf − gfg and \[\frac{f}{g}\] .

 
 

Write the domain and range of the function  \[f\left( x \right) = \frac{x - 2}{2 - x}\] .

 

Write the domain and range of function f(x) given by

\[f\left( x \right) = \frac{1}{\sqrt{x - \left| x \right|}}\] .
 

Let f(x) = |x − 1|. Then,


Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =


The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =


If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are


The domain of the function

\[f\left( x \right) = \sqrt{2 - 2x - x^2}\] is
 

The domain of definition of  \[f\left( x \right) = \sqrt{4x - x^2}\] is 

 

Check if the following relation is function:


Which of the following relations are functions? If it is a function determine its domain and range:

{(1, 1), (3, 1), (5, 2)}


Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 2), (2, −1), (3, 1), (4, 3)}


Check the injectivity and surjectivity of the following function.

f : N → N given by f(x) = x3


Express the following logarithmic equation in exponential form

`log_5  1/25` = – 2


Express the following logarithmic equation in exponential form

In `1/2` = – 0.693


Prove that logbm a = `1/"m" log_"b""a"`


Answer the following:

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


Answer the following:

Let f : R – {2} → R be defined by f(x) = `(x^2 - 4)/(x - 2)` and g : R → R be defined by g(x) = x + 2. Examine whether f = g or not


Answer the following:

If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`


Answer the following:

If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy


Answer the following:

Find value of `(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`


Answer the following:

Find the range of the following function.

f(x) = `x/(9 + x^2)`


A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2


The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Length ‘x’ of
forehand (in cm)
Height 'y' 
(in inches)
35 56
45 65
50 69.5
55 74

Check if this relation is a function


If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.


Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3


If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)


Domain of `sqrt(a^2 - x^2)  (a > 0)` is ______.


If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.


The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.


The period of the function

f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×