मराठी

Let f(x) = x and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x) - Mathematics

Advertisements
Advertisements

प्रश्न

Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find `(f/g)(x)`

बेरीज

उत्तर

`(f/g)(x) = (f(x))/(g(x))`

⇒ `(f/g)(x) = sqrt(x)/x`

Multiplying and dividing by `sqrt(x)`

We get

= `sqrt(x)/x xx sqrt(x)/sqrt(x)`

= `x/(xsqrt(x))`

⇒ `(f/g)(x) = 1/sqrt(x)`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Relations and Functions - Exercise [पृष्ठ ३०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 2 Relations and Functions
Exercise | Q 21.(iv) | पृष्ठ ३०

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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

 

 


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.


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


Let f(x) = |x − 1|. Then,


The range of f(x) = cos [x], for π/2 < x < π/2 is


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


If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are


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 definition of  \[f\left( x \right) = \sqrt{4x - x^2}\] is 

 

The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is

 

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


If ƒ(m) = m2 − 3m + 1, find f(x + 1)


If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`


Find the domain and range of the following function.

f(x) = `root(3)(x + 1)`


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


Write the following expression as a single logarithm.

`1/3 log (x - 1) + 1/2 log (x)`


Prove that logbm a = `1/"m" log_"b""a"`


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


Solve for x.

2 log10 x = `1 + log_10 (x + 11/10)`


Answer the following:

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


Answer the following:

If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`


Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x2 + 1} is a function from X to N?


Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`


Domain of `sqrt(a^2 - x^2)  (a > 0)` is ______.


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


The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.


Range of the function f(x) = `x/(1 + x^2)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×