हिंदी

Write the Domain and Range of Function F(X) Given by F ( X ) = 1 √ X − | X | . - Mathematics

Advertisements
Advertisements

प्रश्न

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

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

उत्तर

Given:

\[f\left( x \right) = \frac{1}{\sqrt{x - \left| x \right|}}\] We know that \[\left| x \right| = \begin{cases}x, & if x \geq 0 \\ - x, & if x < 0\end{cases}\] \[\Rightarrow x - \left| x \right| = \begin{cases}x - x = 0, & if x \geq 0 \\ x + x = 2x, & if x < 0\end{cases}\]
⇒ x - | x| ≤ 0 for all x.
\[\Rightarrow \frac{1}{\sqrt{x - \left| x \right|}}\] does not take any real values for any x ∈ R.
⇒ f (x) is not defined for any x ∈ R.

Hence,
domain ( f ) = Φ and range ( ) = Φ 

 


 
 
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Functions - Exercise 3.5 [पृष्ठ ४२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 3 Functions
Exercise 3.5 | Q 12 | पृष्ठ ४२

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:

(a) range of f, i.e. f(A).


Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:

(b) pre-images of 6, −3 and 5.

 

Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(a) the image set of the domain of f


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

(i) f(x) = x2

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.

(b) f2 = {(1, 1), (2, 7), (3, 5)}


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

(i) \[f\left( \frac{1}{x} \right) = - f\left( x \right)\]

(ii) \[f\left( - \frac{1}{x} \right) = - \frac{1}{f\left( x \right)}\]


If for non-zero xaf(x) + bf \[\left( \frac{1}{x} \right) = \frac{1}{x} - 5\] , where a ≠ b, then find f(x).

 

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: 

(i) f + 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) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .

 

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


If : [−2, 2] → R is defined by \[f\left( x \right) = \begin{cases}- 1, & \text{ for }  - 2 \leq x \leq 0 \\ x - 1, & \text{ for }   0 \leq x \leq 2\end{cases}\] , then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =

 

The range of  \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is 

 


Which of the following relations are functions? 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)}


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

{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}


Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`


Express the area A of circle as a function of its radius r


Express the area A of circle as a function of its circumference C.


Express the following exponential equation in logarithmic form

231 = 23


Write the following expression as sum or difference of logarithm

In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`


Write the following expression as a single logarithm.

ln (x + 2) + ln (x − 2) − 3 ln (x + 5)


Prove that `"b"^(log_"b""a"` = a


Prove that alogcb = blogca


Answer the following:

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

{(12, 1), (3, 1), (5, 2)}


Answer the following:

A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5


Answer the following:

Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph


Answer the following:
If log3 [log2 (log3x)] = 1, show that x = 6561

Answer the following:

Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3


Answer the following:

If a2 = b3 = c4 = d5, show that loga bcd = `47/30`


Find the domain of the following function.

f(x) = `sqrtlog(x^2 - 6x + 6)`


The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.


Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______ 


If a function f(x) is given as f(x) = x2 – 6x + 4 for all x ∈ R, then f(–3) = ______.


Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.


Find the range of the following functions given by f(x) = 1 – |x – 2| 


Find the range of the following functions given by f(x) = 1 + 3 cos2x

(Hint: –1 ≤ cos 2x ≤ 1 ⇒ –3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4)


The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.


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 ______.


Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×