हिंदी

Select the correct answer from given alternatives. Find x, if 2log2 x = 4 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct answer from given alternatives.

Find x, if 2log2 x = 4

विकल्प

  • 4, −4

  • 4

  • −4

  • not defined

MCQ

उत्तर

4

Explanation:

2 log2 x = 4, x > 0

∴ log2 (x2) = 4

∴ x2 = 16

∴ x = ± 4

∴ x = 4

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Miscellaneous Exercise 6.1 [पृष्ठ १२९]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Miscellaneous Exercise 6.1 | Q I. (3) | पृष्ठ १२९

संबंधित प्रश्न

Find the domain of the function  f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`


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

(c) whether f(xy) = f(x) : f(y) holds

 

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

(i) f(x) = x2

Find the range of function.

 

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: 

(vi)  \[2f - \sqrt{5} g\]

 

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

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

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

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 f and g be two functions given by

f = {(2, 4), (5, 6), (8, −1), (10, −3)} and g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, −5)}.

Find the domain of f + g


If  \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and}  g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to

 


If f(x) = cos (loge x), then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right) - \frac{1}{2}\left\{ f\left( xy \right) + f\left( \frac{x}{y} \right) \right\}\] is equal to

 

Check if the following relation is function:


If f(m) = m2 − 3m + 1, find `f(1/2)`


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


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`


Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x3 


Write the following expression as sum or difference of logarithm

`log (sqrt(x) root(3)(y))`


If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b


Solve for x.

log2 x + log4 x + log16 x = `21/4`


Solve for x.

x + log10 (1 + 2x) = x log10 5 + log10 6


If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)


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}


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


Answer the following:

If `log (("a" + "b")/2) = 1/2(log"a" + log"b")`, then show that a = b


Answer the following:

If b2 = ac. prove that, log a + log c = 2 log b


Answer the following:

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


Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?


Given the function f: x → x2 – 5x + 6, evaluate f(– 1)


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 x such that f(x) = 0


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

Check if this relation is a function


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 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 f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.


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


The range of the function y = `1/(2 - sin3x)` is ______.


The function f: R `rightarrow` R defined by f(x) = sin x is ______.


Which of the following functions is NOT one-one?


The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×