हिंदी

Let F(X) = X, G ( X ) = 1 X and H(X) = F(X) G(X). Then, H(X) = 1(a) x ∈ R (b) x ∈ Q (c) x ∈ R − Q (d) x ∈ R, x ≠ 0 - Mathematics

Advertisements
Advertisements

प्रश्न

Let f(x) = x, \[g\left( x \right) = \frac{1}{x}\]  and h(x) = f(xg(x). Then, h(x) = 1

विकल्प

  • (a) x ∈ R

  • (b) x ∈ Q

  • (c) x ∈ R − Q

  • (d) x ∈ R, x ≠ 0

     
MCQ

उत्तर

(d) x ∈ R, x ≠ 0

Given:
f(x) = x,  \[g\left( x \right) = \frac{1}{x}\]  and h(x) = f(xg(x) Now,
\[h(x) = x \times \frac{1}{x} = 1\] We observe that the domain of f is \[\mathbb{R}\] and the domain of g is  \[\mathbb{R} - \left\{ 0 \right\}\] ∴ Domain of h = Domain of f ⋂ Domain of g = \[\mathbb{R} \cap \left[ \mathbb{R} - \left\{ 0 \right\} \right] = \mathbb{R} - \left\{ 0 \right\}\]
\[\Rightarrow\] x ∈ R, x ≠ 0
 
 
 
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Functions - Exercise 3.6 [पृष्ठ ४४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 3 Functions
Exercise 3.6 | Q 19 | पृष्ठ ४४

वीडियो ट्यूटोरियलVIEW ALL [1]

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).


The function f is defined by \[f\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 3 \\ 3x, & 3 \leq x \leq 10\end{cases}\]

The relation g is defined by \[g\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 2 \\ 3x, & 2 \leq x \leq 10\end{cases}\]

Show that f is a function and g is not a 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)  \[2f - \sqrt{5} g\]

 

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: 

(viii) \[\frac{5}{8}\]

 

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

(ii) fg


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

 

 


Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.


The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is


If f(m) = m2 − 3m + 1, find f(0)


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

x2 − y = 25


Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6


An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain


Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x2 


Express the following exponential equation in logarithmic form

10−2 = 0.01


Express the following exponential equation in logarithmic form

`"e"^(1/2)` = 1.6487


Express the following logarithmic equation in exponential form

ln e = 1


Write the following expression as a single logarithm.

5 log x + 7 log y − log z


Write the following expression as a single logarithm.

ln (x + 2) + ln (x − 2) − 3 ln (x + 5)


Prove that `"b"^(log_"b""a"` = a


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


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


Answer the following:

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


Answer the following:

If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy


Answer the following:

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


Answer the following:

Show that, logy x3 . logz y4 . logx z5 = 60


Answer the following:

Find the range of the following function.

f(x) = |x – 5|


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 Range


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


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


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


Find the range of the following functions given by f(x) = 1 – |x – 2| 


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 real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.


The domain of the function f(x) = `sin^-1((|x| + 5)/(x^2 + 1))` is (–∞, –a] ≈ [a, ∞). Then a is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×