Advertisements
Advertisements
प्रश्न
Express the following exponential equation in logarithmic form
`9^(3/2)` = 27
उत्तर
Exponential form | Logarithmic form |
`9^(3/2)` = 27 | `3/2` = log9 27 |
APPEARS IN
संबंधित प्रश्न
Find the domain of the function f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
What is the fundamental difference between a relation and a function? Is every relation a function?
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(a) range of f, i.e. f(A).
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 \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
If for non-zero x, af(x) + bf \[\left( \frac{1}{x} \right) = \frac{1}{x} - 5\] , where a ≠ b, then find f(x).
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
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
Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
Which one of the following is not a function?
If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to
If f : [−2, 2] → R is defined by \[f\left( x \right) = \begin{cases}- 1, & \text{ for } - 2 \leq x \leq 0 \\ x - 1, & \text{ for } 0 \leq x \leq 2\end{cases}\] , then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =
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, 1), (2, 1), (3, 1), (4, 1)}
If f(m) = m2 − 3m + 1, find f(− x)
Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2
Find the domain and range of the following function.
g(x) = `(x + 4)/(x - 2)`
Express the area A of circle as a function of its radius r
lf f(x) = 3(4x+1), find f(– 3)
Solve for x.
log2 + log(x + 3) – log(3x – 5) = log3
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 ______.
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Select the correct answer from given alternative.
The domain and range of f(x) = 2 − |x − 5| is
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
Answer the following:
Find the range of the following function.
f(x) = [x] – x
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
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 function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
Find the domain of the following function.
f(x) = [x] + x
Find the range of the following functions given by `sqrt(16 - x^2)`
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 function given by:
f(x) = `(3x)/(2x - 8)`
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f + g)(x)
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.