Advertisements
Advertisements
प्रश्न
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
पर्याय
(a) (−∞, −3] ∪ (2, 5)
(b) (−∞, −3) ∪ (2, 5)
(c) (−∞, −3) ∪ [2, 5]
(d) None of these
उत्तर
(a) (−∞, −3] ∪ (2, 5)
\[ \text{ For f(x) to be defined ,} \]
\[\left( 2 - x \right)\left( x - 5 \right) \neq 0\]
\[ \Rightarrow x \neq 2, 5 . . . . (1)\]
\[\text{ Also } , \frac{\left( x + 3 \right)}{\left( 2 - x \right)\left( x - 5 \right)} \geq 0\]
\[ \Rightarrow \frac{\left( x + 3 \right)\left( 2 - x \right)\left( x - 5 \right)}{\left( 2 - x \right)^2 \left( x - 5 \right)^2} \geq 0\]
\[ \Rightarrow \left( x + 3 \right)\left( x - 2 \right)\left( x - 5 \right) \leq 0\]
\[ \Rightarrow x \in ( - \infty , - 3] \cup (2, 5) . . . . (2)\]
\[\text{ From (1) and (2),} \]
\[x \in ( - \infty , - 3] \cup (2, 5)\]
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].
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
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(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
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:
(vii) f2 + 7f
Write the range of the real function f(x) = |x|.
If f, g, h are real functions given by f(x) = x2, g(x) = tan x and h(x) = loge x, then write the value of (hogof)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
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
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(x) =
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
The domain of the function
The domain of definition of \[f\left( x \right) = \sqrt{x - 3 - 2\sqrt{x - 4}} - \sqrt{x - 3 + 2\sqrt{x - 4}}\] is
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(2)
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(0)
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
If f(m) = m2 − 3m + 1, find `f(1/2)`
If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`
Express the area A of a square as a function of its side s
lf f(x) = 3(4x+1), find f(– 3)
Express the following exponential equation in logarithmic form
10−2 = 0.01
Find the domain of f(x) = ln (x − 5)
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)
Select the correct answer from given alternatives.
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.
Answer the following:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3
Answer the following:
Find x, if x = 33log32
Answer the following:
If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)
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?
A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/2`
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 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 a and b
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
Let f : R → R be defined by
f(x) = `{(3x; x > 2),(2x^2; 1 ≤ x ≤ 2), (4x; x < 1):}`
Then f(-2) + f(1) + f(3) is ______
The domain and range of the real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
