Advertisements
Advertisements
प्रश्न
Answer the following:
For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3
उत्तर
L.H.S. = log (1 + 2 + 3) = log 6
R.H.S. = log 1 + log 2 + log 3
= 0 + log (2 × 3)
= log 6
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
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 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).
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
If \[f\left( x \right) = \begin{cases}x^2 , & \text{ when } x < 0 \\ x, & \text{ when } 0 \leq x < 1 \\ \frac{1}{x}, & \text{ when } x \geq 1\end{cases}\]
find: (a) f(1/2), (b) f(−2), (c) f(1), (d)
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:
(iv) \[\frac{f}{g}\]
Write the range of the real function f(x) = |x|.
Write the domain and range of function f(x) given by
The range of f(x) = cos [x], for π/2 < x < π/2 is
The domain of the function \[f\left( x \right) = \sqrt{\frac{\left( x + 1 \right) \left( x - 3 \right)}{x - 2}}\] is
The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
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)}
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`
Find the domain and range of the following function.
g(x) = `(x + 4)/(x - 2)`
Write the following expression as sum or difference of logarithm
`log (sqrt(x) root(3)(y))`
Solve for x.
2 log10 x = `1 + log_10 (x + 11/10)`
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range
{(12, 1), (3, 1), (5, 2)}
Answer the following:
A function f : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f–1
Answer the following:
If f(x) = 3x4 – 5x2 + 7 find f(x – 1)
Answer the following:
If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - 3) + 1/(log(5 - x))`
Answer the following:
Find the range of the following function.
f(x) = |x – 5|
Given the function f: x → x2 – 5x + 6, evaluate f(2a)
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Range
A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/2`
A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
If f(x) = `(x - 1)/(x + 1)`, then show that `f(- 1/x) = (-1)/(f(x))`
Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x, and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ______.
The function f: R `rightarrow` R defined by f(x) = sin x is ______.
Let f(θ) = sin θ (sin θ + sin 3θ) then ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.
