Advertisements
Advertisements
प्रश्न
Answer the following:
Find x, if x = 33log32
उत्तर
x = 33log32 = (3log32)3
= (2)3 ...[∵ alogax = x]
= 8.
APPEARS IN
संबंधित प्रश्न
If f(x) = x2, find `(f(1.1) - f(1))/((1.1 - 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?
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.
(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?
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:
(iii) f g
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 : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
If f(x) = 4x − x2, x ∈ R, then write the value of f(a + 1) −f(a − 1).
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 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 \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
If \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,
The domain of definition of the function \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(2)
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 3), (4, 1), (2, 2)}
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`
If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b
Find the domain and range of the following function.
f(x) = 7x2 + 4x − 1
Express the area A of circle as a function of its diameter d
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Answer the following:
If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy
Answer the following:
Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Given the function f: x → x2 – 5x + 6, evaluate f(2)
A graph representing the function f(x) is given in it is clear that f(9) = 2
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
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 graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Range
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
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
The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
Find the domain of the following functions given by f(x) = x|x|
Find the domain of the following function given by:
f(x) = `(3x)/(2x - 8)`
The domain of the function f(x) = `sin^-1((|x| + 5)/(x^2 + 1))` is (–∞, –a] ≈ [a, ∞). Then a is equal to ______.