Advertisements
Advertisements
प्रश्न
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.
उत्तर
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is {2, 8, 10}.
Explanation:
Since Domain of f = Df
= {2, 5, 8, 10}
And Domain of g = Dg
= {2, 7, 8, 10, 11}
Therefore the domain of f + g = {x | x ∈ Df ∩ Dg}
= {2, 8, 10}
APPEARS IN
संबंधित प्रश्न
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.
If \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
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:
(iv) \[\frac{f}{g}\]
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(x) = cos (log x), then the value of f(x2) f(y2) −
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
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
Let f(x) = x, \[g\left( x \right) = \frac{1}{x}\] and h(x) = f(x) g(x). Then, h(x) = 1
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(x) =
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
Which of the following relations are functions? If it is a function determine its domain and range:
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(2)
Find the domain of f(x) = ln (x − 5)
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
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:
If f(x) = 3x + a and f(1) = 7 find a and f(4)
Answer the following:
Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph
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:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
Given the function f: x → x2 – 5x + 6, evaluate f(2a)
A graph representing the function f(x) is given in it is clear that f(9) = 2
What is the image of 6 under f?
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
Find the domain of the following functions given by f(x) = x|x|
Find the range of the following functions given by f(x) = 1 – |x – 2|
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.