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Express the area A of circle as a function of its radius r - Mathematics and Statistics

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प्रश्न

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

एक पंक्ति में उत्तर

उत्तर

If r is the radius of the circle, then area A is given by A = `pi"r"^2`

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अध्याय 6: Functions - Exercise 6.1 [पृष्ठ ११८]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Exercise 6.1 | Q 10. (a) | पृष्ठ ११८

संबंधित प्रश्न

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

  1. {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
  2. {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
  3. {(1, 3), (1, 5), (2, 5)}

A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [yf(y) = −1].


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


et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.


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


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

 

 


Write the range of the real function f(x) = |x|.

 

If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]

for all x ∈ R − {0}, then write the expression for f(x).

 
 

If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]

 

 


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

 

Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by  \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (is


If  \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =

 

The domain of definition of the function \[f\left( x \right) = \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{1 - x}{1 + x}}\] is 

 

The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is

 

Check if the following relation is function:


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) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x


Find x, if g(x) = 0 where g(x) = 6x2 + x − 2


Find the domain and range of the following function.

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


Express the area A of a square as a function of its side s


Express the area A of circle as a function of its diameter d


Show that if f : A → B and g : B → C are onto, then g ° f is also onto


Express the following exponential equation in logarithmic form

e–x = 6


Write the following expression as sum or difference of logarithm

In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`


Select the correct answer from given alternatives.

Find x, if 2log2 x = 4


Select the correct answer from given alternatives.

If f(x) =`1/(1 - x)`, then f{f[f(x)]} is


Answer the following:

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

 Describe the following Domain


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


The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.


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


Let A and B be any two sets such that n(B) = p, n(A) = q then the total number of functions f : A → B is equal to ______.


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 ______.


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


The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.


The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval


The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.


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


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