हिंदी

Answer the following: Identify the following relation is the function? If it is a function determine its domain and range {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Answer the following:

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

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

योग

उत्तर

Let f = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

f is a function because every element of domain has only one image.

Domain of f = {2, 4, 6, 8, 10, 12, 14}

Range of f = {1, 2, 3, 4, 5, 6, 7}

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Miscellaneous Exercise 6.2 [पृष्ठ १३०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Miscellaneous Exercise 6.2 | Q II. (1) (i) | पृष्ठ १३०

संबंधित 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?


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)}

 

 


If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).

 

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

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

 

If f(x) = loge (1 − x) and g(x) = [x], then determine function:

(i) f + g

 


If f(x) = loge (1 − x) and g(x) = [x], then determine function:

(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),

\[\left( \frac{f}{g} \right) \left( \frac{1}{2} \right), \left( \frac{g}{f} \right) \left( \frac{1}{2} \right)\]
 
 

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


Let  \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] . Then write the value of α satisfying f(f(x)) = x for all x ≠ −1.

 

 


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

 

 


Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.


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

  

The domain of definition of the function  \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is

 

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


Check if the following relation is a function.


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

x2 − y = 25


If f(m) = m2 − 3m + 1, find f(−3)


Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2


Check the injectivity and surjectivity of the following function.

f : Z → Z given by f(x) = x2 


Write the following expression as sum or difference of logarithm

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


Write the following expression as a single logarithm.

5 log x + 7 log y − log z


If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7


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:

Find whether the following function is one-one

f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)` for x ∈ R − {3}


Answer the following:

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


Answer the following:

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


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) = `1/(1 + sqrt(x))`


The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______


If f(x) = 5x - 3, then f-1(x) is ______ 


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 domain of the following functions given by f(x) = x|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 real function f defined by f(x) = `sqrt(x - 1)` is given by ______.


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


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


Which of the following functions is NOT one-one?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×