हिंदी

A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3

योग

उत्तर

f(x) = 5 – x for 0 ≤ x ≤ 4

f(x) = 3

∴ 5 – x = 3

∴ x = 2.

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. (7) (i) | पृष्ठ १३०

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).


If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.

 

 


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

(ii) fg


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

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

Let f and g be two real functions given by

f = {(0, 1), (2, 0), (3, −4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}

Find the domain of fg.


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


f is a real valued function given by \[f\left( x \right) = 27 x^3 + \frac{1}{x^3}\] and α, β are roots of \[3x + \frac{1}{x} = 12\] . Then,

 
 

The domain of the function

\[f\left( x \right) = \sqrt{2 - 2x - x^2}\] is
 

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 the function \[f\left( x \right) = \sqrt{\frac{\left( x + 1 \right) \left( x - 3 \right)}{x - 2}}\] is

  

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

 

The range of the function f(x) = |x − 1| is


Check if the following relation is function:


If ƒ(m) = m2 − 3m + 1, find f(x + 1)


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


Check the injectivity and surjectivity of the following function.

f : Z → Z given by f(x) = x2 


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


Express the following logarithmic equation in exponential form

ln e = 1


Find the domain of f(x) = log10 (x2 − 5x + 6)


Prove that alogcb = blogca


Select the correct answer from given alternatives.

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


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:

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 : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f–1


Answer the following:

For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3


Answer the following:

Solve for x, logx (8x – 3) – logx 4 = 2


Answer the following:

Find the range of the following function.

f(x) = 1 + 2x + 4x 


Answer the following:

Find (f ° g) (x) and (g ° f) (x)

f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`


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

 Describe the following Domain


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


A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2


A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour


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 length of forehand of a person if the height is 53.3 inches


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


The domain of the function f(x) = log3+x (x2 - 1) is ______.


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


Find the domain of the following function.

f(x) = [x] + x


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 ______.


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)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.