Advertisements
Advertisements
प्रश्न
Find the domain and range of the following function.
f(x) = `sqrt((x - 3)/(7 - x))`
उत्तर
f(x) = `sqrt((x - 3)/(7 - x))`
f(x) is defined, if `(x - 3)/(7 - x)` ≥ 0 and x ≠ 7
`(x - 3)/(7 - x)` ≥ 0, if x – 3 ≥ 0 and 7 – x > 0
or x – 3 ≤ 0 and 7 – x < 0
If x – 3 ≤ 0 and 7 – x < 0, then
x ≤ 3 and 7 < x
i.e., x ≤ 3 and x > 7
This is not possible.
∴ `(x - 3)/(7 - x)` ≥ 0, if x – 3 ≥ 0 and 7 – x > 0
i.e., if x ≥ 3 and 7 > x
i.e., if 3 ≤ x < 7
∴ Domian = {x/x ∈ R, 3 ≤ x < 7}
= [3, 7)
Let y = `sqrt((x - 3)/(7 - x))` ≥ 0 for all x ∈ [3, 7)
∴ Range = `[0, ∞)`
∴ Domian = [3, 7), Range = `[0, ∞)`
APPEARS IN
संबंधित प्रश्न
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
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) \[\frac{g}{f}\]
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
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]
If f(x) = cos (log x), then the value of f(x) f(y) −\[\frac{1}{2}\left\{ f\left( \frac{x}{y} \right) + f\left( xy \right) \right\}\] is
Let f(x) = |x − 1|. Then,
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and} g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to
If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
If \[\left[ x \right]^2 - 5\left[ x \right] + 6 = 0\], where [.] denotes the greatest integer function, then
Check if the following relation is function:
Which of the following relations are functions? If it is a function determine its domain and range:
{(1, 1), (3, 1), (5, 2)}
If f(x) = 3x + a and f(1) = 7 find a and f(4).
If f(m) = m2 − 3m + 1, find `f(1/2)`
If f(m) = m2 − 3m + 1, find f(x + 1)
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Prove that logbm a = `1/"m" log_"b""a"`
Prove that alogcb = blogca
If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
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 `log (("a" + "b")/2) = 1/2(log"a" + log"b")`, then show that a = b
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
A graph representing the function f(x) is given in it is clear that f(9) = 2
For what value of x is f(x) = 1?
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))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 |
Find the height of a person whose forehand length is 40 cm
A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
The domain of the function f(x) = `sqrtx` is ______.
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
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 ______.
Find the domain of the following functions given by f(x) = x|x|
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.
Range of the function f(x) = `x/(1 + x^2)` is ______.
