हिंदी

Let F : R → R and G : C → C Be Two Functions Defined as F(X) = X2 and G(X) = X2. Are They Equal Functions? - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

It is given that
f : R → R and g : C → C are two function defined as (x) = x2 and (x) = x2 .
Thus,
domain ( ) = R and domain ( ) = C .
Since, domain ( ) ≠ domain ( g ),
 (x) and (x) are not equal functions.

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 9 | पृष्ठ ८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Define a function as a correspondence between two sets.

 

fgh are three function defined from R to R as follow:

(ii) g(x) = sin x

Find the range of function.


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.

(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)} 


If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]


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: 

(ii) g − 


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: 

(v) \[\frac{g}{f}\]

 

Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] . 


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

 

If f(x) = cos (log x), then the value of f(xf(y) −\[\frac{1}{2}\left\{ f\left( \frac{x}{y} \right) + f\left( xy \right) \right\}\] is

 

If  \[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] for x ∈ R, then f (2002) = 


If  \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,

 

The domain of definition of  \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is 

  

The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is


If f(m) = m2 − 3m + 1, find f(− x)


If f(x) = 3x + a and f(1) = 7 find a and f(4).


If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.


If f(x) = `{(x^2 + 3","  x ≤ 2),(5x + 7","  x > 2):},` then find f(2)


Check if the relation given by the equation represents y as function of x:

2x + 3y = 12


Check if the relation given by the equation represents y as function of x:

2y + 10 = 0


Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`


Express the following logarithmic equation in exponential form

ln 1 = 0


Solve for x.

log2 + log(x + 3) – log(3x – 5) = log3


If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)


Answer the following:

Identify the following relation is the function? If it is a function determine its domain and range.

{(0, 0), (1, 1), (1, –1), (4, 2), (4, –2), (9, 3), (9, –3), (16, 4), (16, –4)}


Answer the following:

If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - x^2) + sqrt(5 - x)`


Answer the following:

Find the range of the following function.

f(x) = |x – 5|


Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?


Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)


A graph representing the function f(x) is given in it is clear that f(9) = 2

 Describe the following Domain


The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`

 Calculate the value of `"gg" (1/2)`


If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.


Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f – g)(x)


Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x)


The domain and range of the real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.


The ratio `(2^(log_2  1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.


Let f(θ) = sin θ (sin θ + sin 3θ) then ______.


lf f : [0, ∞) `rightarrow` [0, ∞) and f(x) = `x/(1 + x)`, then f 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×