हिंदी

Check if the relation given by the equation represents y as function of x: 2x + 3y = 12 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

2x + 3y = 12

योग

उत्तर

2x + 3y = 12

∴ y = `(12 - 2x)/3`

∴ For every value of x, there is a unique value of y.

∴ y is a function of x.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Exercise 6.1 [पृष्ठ ११८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Exercise 6.1 | Q 3. (a) | पृष्ठ ११८

संबंधित प्रश्न

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


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

 

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

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

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


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: 

(iii) f g


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

(ii) fg


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


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(x) = log |x| is


Let  \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?

 


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


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

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


Find the domain and range of the follwoing function.

h(x) = `sqrt(x + 5)/(5 + x)`


Express the following logarithmic equation in exponential form

ln 1 = 0


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


If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy 


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


Select the correct answer from given alternatives.

If f : R → R is defined by f(x) = x3 then f–1 (8) is equal to :


Select the correct answer from given alternative.

The domain and range of f(x) = 2 − |x − 5| is


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:

A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist


Answer the following:

Find x, if x = 33log32  


Answer the following:

Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2


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:

If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1


Answer the following:

If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k


Answer the following:

Find the domain of the following function.

f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`


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

For what value of x is f(x) = 1?


A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/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

Find the height of a person whose forehand length is 40 cm


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

 Calculate the value of `"gg" (1/2)`


Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f(x) = x3 then, find the range of f


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


If f(x) = `1/sqrt(4 - 3x)`, then dom(f) = ______..


Find the domain of the following functions given by f(x) = x|x|


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


The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×