Advertisements
Advertisements
प्रश्न
The domain of definition of \[f\left( x \right) = \sqrt{4x - x^2}\] is
विकल्प
(a) R − [0, 4]
(b) R − (0, 4)
(c) (0, 4)
(d) [0, 4]
उत्तर
(d) [0, 4]
⇒ x(4 - x) ≥ 0
⇒ x(x -4) ≤ 0
⇒ x ∈ [0, 4]
Hence, domain (f )= [0, 4].
APPEARS IN
संबंधित प्रश्न
Define a function as a correspondence between two sets.
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
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:
(i) f + g
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(ii) fg
Write the range of the real function f(x) = |x|.
Write the range of the function f(x) = ex−[x], x ∈ R.
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 A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(3)
Check if the following relation is a function.
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)}
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 1), (2, 1), (3, 1), (4, 1)}
Check if the relation given by the equation represents y as function of x:
2x + 3y = 12
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6
Express the area A of a square as a function of its side s
Express the area A of circle as a function of its diameter d
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
`"e"^(1/2)` = 1.6487
Express the following exponential equation in logarithmic form
e–x = 6
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
Express the following logarithmic equation in exponential form
ln 1 = 0
Write the following expression as sum or difference of logarithm
In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
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:
If f(x) = 3x + a and f(1) = 7 find a and f(4)
Answer the following:
Solve for x, logx (8x – 3) – logx 4 = 2
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
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?
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
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 domain of the function f(x) = log3+x (x2 - 1) is ______.
Find the domain of the following function.
f(x) = [x] + x
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x, and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ______.
lf f : [0, ∞) `rightarrow` [0, ∞) and f(x) = `x/(1 + x)`, then f is ______.