Advertisements
Advertisements
प्रश्न
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
उत्तर
L.H.S. = `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|`
= `log |(sqrt(x^2 + 1) + x) (sqrt(x^2 + 1) - x)|`
= log |x2 + 1 – x2|
= log 1
= 0
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
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)
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(ii) fg
If f, g and h are real functions defined by
Write the range of the real function f(x) = |x|.
Let \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] . Then write the value of α satisfying f(f(x)) = x for all x ≠ −1.
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)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
The range of f(x) = cos [x], for π/2 < x < π/2 is
The domain of the function
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 definition of the function f(x) = log |x| is
Check if the following relation is function:
Check if the following relation is a function.
Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`
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
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
Solve for x.
x + log10 (1 + 2x) = x log10 5 + log10 6
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Answer the following:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
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 – 5|
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
Given the function f: x → x2 – 5x + 6, evaluate f(– 1)
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
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 ______.
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f – g)(x)
The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval
lf f : [0, ∞) `rightarrow` [0, ∞) and f(x) = `x/(1 + x)`, then f is ______.
