Advertisements
Advertisements
Question
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
Options
(– a, a)
[– a, a]
[0, a]
(– a, 0]
Solution
Domain of `sqrt(a^2 - x^2) (a > 0)` is [– a, a].
Explanation:
Let f(x) = `sqrt(a^2 - x^2)`
f(x) is defined if a2 – x2 ≥ 0
⇒ x2 – a2 ≤ 0
⇒ x2 ≤ a2
⇒ x ≤ ± a
⇒ – a ≤ x ≤ a
∴ Domain of f(x) = [– a, a]
APPEARS IN
RELATED QUESTIONS
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
- {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
- {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
- {(1, 3), (1, 5), (2, 5)}
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.
(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}
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:
(v) \[\frac{g}{f}\]
If f(x) = cos [π2]x + cos [−π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(x) =
The domain of definition of the function f(x) = log |x| 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)}
A function f is defined as follows: f(x) = 4x + 5, for −4 ≤ x < 0. Find the values of f(−1), f(−2), f(0), if they exist.
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
Show that if f : A → B and g : B → C are onto, then g ° f is also onto
Express the following exponential equation in logarithmic form
25 = 32
Write the following expression as sum or difference of logarithm
`log (sqrt(x) root(3)(y))`
Write the following expression as sum or difference of logarithm
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Answer the following:
Find the domain of the following function.
f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
If f(x) = `1/sqrt(4 - 3x)`, then dom(f) = ______..
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.
Find the domain of the following function given by:
f(x) = `(3x)/(2x - 8)`
Find the range of the following functions given by f(x) = 1 + 3 cos2x
(Hint: –1 ≤ cos 2x ≤ 1 ⇒ –3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4)
If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval
